iCON Education

2017 Q151 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

The two adjacent sides of a cyclic quadrilateral are 2 and 5 and the angle between them is 60^o. If the area of the quadrilateral is $4\sqrt 3 $, then the perimeter of the quadrilateral is :

A.

12.5

B.

13.2

C.

12

D.

13

2017 Q152 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

A line drawn through the point P(4, 7) cuts the circle x² + y² = 9 at the points A and B. Then PA⋅PB is equal to :

A.

53

B.

56

C.

74

D.

65

2017 Q153 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

If two parallel chords of a circle, having diameter 4units, lie on the opposite sides of the center and subtend angles ${\cos ^{ - 1}}\left( {{1 \over 7}} \right)$ and sec^$-$1 (7) at the center respectivey, then the distance between these chords, is :

A.

${4 \over {\sqrt 7 }}$

B.

${8 \over {\sqrt 7 }}$

C.

${8 \over 7}$

D.

${16 \over 7}$

2017 Q154 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

If a point P has co-ordinates (0, $-$2) and Q is any point on the circle, x² + y² $-$ 5x $-$ y + 5 = 0, then the maximum value of (PQ)² is :

A.

${{25 + \sqrt 6 } \over 2}$

B.

14 + $5\sqrt 3 $

C.

${{47 + 10\sqrt 6 } \over 2}$

D.

8 + 5$\sqrt 3 $

2017 Q155 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

The radius of a circle, having minimum area, which touches the curve y = 4 – x² and the lines, y = |x| is :

A.

$2\left( {\sqrt 2 - 1} \right)$

B.

$4\left( {\sqrt 2 - 1} \right)$

C.

$4\left( {\sqrt 2 + 1} \right)$

D.

$2\left( {\sqrt 2 + 1} \right)$

2016 Q156 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

Equation of the tangent to the circle, at the point (1, −1), whose centre is the point of intersection of the straight lines x − y = 1 and 2x + y = 3 is :

A.

4x + y − 3 = 0

B.

x + 4y + 3 = 0

C.

3x − y − 4 = 0

D.

x − 3y − 4 = 0

2016 Q157 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

A circle passes through (−2, 4) and touches the y-axis at (0, 2). Which one of the following equations can represent a diameter of this circle?

A.

4x + 5y − 6 = 0

B.

2x − 3y + 10 = 0

C.

3x + 4y − 3 = 0

D.

5x + 2y + 4 = 0

2016 Q158 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

If one of the diameters of the circle, given by the equation, ${x^2} + {y^2} - 4x + 6y - 12 = 0,$ is a chord of a circle $S$, whose centre is at $(-3, 2)$, then the radius of $S$ is :

A.

$5$

B.

$10$

C.

$5\sqrt 2 $

D.

$5\sqrt 3 $

2016 Q159 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

The centres of those circles which touch the circle, ${x^2} + {y^2} - 8x - 8y - 4 = 0$, externally and also touch the $x$-axis, lie on :

A.

a circle

B.

an ellipse which is not a circle

C.

a hyperbola

D.

a parabola

2015 Q160 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

Locus of the image of the point $(2, 3)$ in the line $\left( {2x - 3y + 4} \right) + k\left( {x - 2y + 3} \right) = 0,\,k \in R,$ is a :

A.

circle of radius $\sqrt 2 $.

B.

circle of radius $\sqrt 3 $.

C.

straight line parallel to $x$-axis

D.

straight line parallel to $y$-axis

2015 Q161 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

The number of common tangents to the circles ${x^2} + {y^2} - 4x - 6x - 12 = 0$ and ${x^2} + {y^2} + 6x + 18y + 26 = 0,$ is :

A.

$3$

B.

$4$

C.

$1$

D.

$2$

2014 Q162 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

Let $C$ be the circle with centre at $(1, 1)$ and radius $=$ $1$. If $T$ is the circle centred at $(0, y)$, passing through origin and touching the circle $C$ externally, then the radius of $T$ is equal to :

A.

${1 \over 2}$

B.

${1 \over 4}$

C.

${{\sqrt 3 } \over {\sqrt 2 }}$

D.

${{\sqrt 3 } \over 2}$

2013 Q163 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

The circle passing through $(1, -2)$ and touching the axis of $x$ at $(3, 0)$ also passes through the point :

A.

$\left( { - 5,\,2} \right)$

B.

$\left( { 2,\,-5} \right)$

C.

$\left( { 5,\,-2} \right)$

D.

$\left( { - 2,\,5} \right)$

2012 Q164 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

The length of the diameter of the circle which touches the $x$-axis at the point $(1, 0)$ and passes through the point $(2, 3)$ is :

A.

${{10} \over 3}$

B.

${{3} \over 5}$

C.

${{6} \over 5}$

D.

${{5} \over 3}$

2011 Q165 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

The two circles x² + y² = ax, and x² + y² = c² (c > 0) touch each other if :

A.

| a | = c

B.

a = 2c

C.

| a | = 2c

D.

2 | a | = c

2010 Q166 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

The circle ${x^2} + {y^2} = 4x + 8y + 5$ intersects the line $3x - 4y = m$ at two distinct points if :

A.

$ - 35 < m < 15$

B.

$ 15 < m < 65$

C.

$ 35 < m < 85$

D.

$ - 85 < m < -35$

2009 Q167 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

Three distinct points A, B and C are given in the 2 -dimensional coordinates plane such that the ratio of the distance of any one of them from the point $(1, 0)$ to the distance from the point $(-1, 0)$ is equal to ${1 \over 3}$. Then the circumcentre of the triangle ABC is at the point :

A.

$\left( {{5 \over 4},0} \right)$

B.

$\left( {{5 \over 2},0} \right)$

C.

$\left( {{5 \over 3},0} \right)$

D.

$\left( {0,0} \right)$

2009 Q168 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

If $P$ and $Q$ are the points of intersection of the circles
${x^2} + {y^2} + 3x + 7y + 2p - 5 = 0$ and ${x^2} + {y^2} + 2x + 2y - {p^2} = 0$ then there is a circle passing through $P,Q $ and $(1, 1)$ for :

A.

all except one value of $p$

B.

all except two values of $p$

C.

exactly one value of $p$

D.

all values of $p$

2008 Q169 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

The differential equation of the family of circles with fixed radius $5$ units and centre on the line $y = 2$ is :

A.

$\left( {x - 2} \right){y^2} = 25 - {\left( {y - 2} \right)^2}$

B.

$\left( {y - 2} \right){y^2} = 25 - {\left( {y - 2} \right)^2}$

C.

${\left( {y - 2} \right)^2}{y^2} = 25 - {\left( {y - 2} \right)^2}$

D.

${\left( {x - 2} \right)^2}{y^2} = 25 - {\left( {y - 2} \right)^2}$

2008 Q170 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

The point diametrically opposite to the point $P(1, 0)$ on the circle ${x^2} + {y^2} + 2x + 4y - 3 = 0$ is :

A.

$(3, -4)$

B.

$(-3, 4)$

C.

$(-3, -4)$

D.

$(3, 4)$

2007 Q171 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

Consider a family of circles which are passing through the point $(-1, 1)$ and are tangent to $x$-axis. If $(h, k)$ are the coordinate of the centre of the circles, then the set of values of $k$ is given by the interval :

A.

$ - {1 \over 2} \le k \le {1 \over 2}$

B.

$k \le {1 \over 2}$

C.

$0 \le k \le {1 \over 2}$

D.

$k \ge {1 \over 2}$

2006 Q172 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

If the lines $3x - 4y - 7 = 0$ and $2x - 3y - 5 = 0$ are two diameters of a circle of area $49\pi $ square units, the equation of the circle is :

A.

$\,{x^2} + {y^2} + 2x\, - 2y - 47 = 0\,$

B.

$\,{x^2} + {y^2} + 2x\, - 2y - 62 = 0\,$

C.

${x^2} + {y^2} - 2x\, + 2y - 62 = 0$

D.

${x^2} + {y^2} - 2x\, + 2y - 47 = 0$

2006 Q173 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

Let $C$ be the circle with centre $(0, 0)$ and radius $3$ units. The equation of the locus of the mid points of the chords of the circle $C$ that subtend an angle of ${{2\pi } \over 3}$ at its center is :

A.

${x^2} + {y^2} = {3 \over 2}$

B.

${x^2} + {y^2} = 1$

C.

${x^2} + {y^2} = {{27} \over 4}$

D.

${x^2} + {y^2} = {{9} \over 4}$

2005 Q174 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

If the circles ${x^2}\, + \,{y^2} + \,2ax\, + \,cy\, + a\,\, = 0$ and ${x^2}\, + \,{y^2} - \,3ax\, + \,dy\, - 1\,\, = 0$ intersect in two ditinct points P and Q then the line 5x + by - a = 0 passes through P and Q for :

A.

exactly one value of a

B.

no value of a

C.

infinitely many values of a

D.

exactly two values of a

2005 Q175 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

If the pair of lines $a{x^2} + 2\left( {a + b} \right)xy + b{y^2} = 0$ lie along diameters of a circle and divide the circle into four sectors such that the area of one of the sectors is thrice the area of another sector then :

A.

$3{a^2} - 10ab + 3{b^2} = 0$

B.

$3{a^2} - 2ab + 3{b^2} = 0$

C.

$3{a^2} + 10ab + 3{b^2} = 0$

D.

$3{a^2} + 2ab + 3{b^2} = 0$

2005 Q176 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is :

A.

an ellipse

B.

a circle

C.

a hyperbola

D.

a parabola

2005 Q177 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

If a circle passes through the point (a, b) and cuts the circle ${x^2}\, + \,{y^2} = {p^2}$ orthogonally, then the equation of the locus of its centre is :

A.

${x^2}\, + \,{y^2} - \,3ax\, - \,4\,by\,\, + \,({a^2}\, + \,{b^2} - {p^2}) = 0$

B.

$2ax\, + \,\,2\,by\,\, - \,({a^2}\, - \,{b^2} + {p^2}) = 0$

C.

${x^2}\, + \,{y^2} - \,2ax\, - \,\,3\,by\,\, + \,({a^2}\, - \,{b^2} - {p^2}) = 0$

D.

$2ax\, + \,\,2\,by\,\, - \,({a^2}\, + \,{b^2} + {p^2}) = 0$

2004 Q178 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

A variable circle passes through the fixed point A (p, q) and touches x-axis. The locus of the other end of the diameter through A is :

A.

${(y\, - \,q)^2} = \,4\,px$

B.

${(x\, - \,q)^2} = \,4\,py$

C.

${(y\, - \,p)^2} = \,4\,qx$

D.

${(x\, - \,p)^2} = \,4\,qy$

2004 Q179 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

Intercept on the line y = x by the circle ${x^2}\, + \,{y^2} - 2x = 0$ is AB. Equation of the circle on AB as a diameter is :

A.

$\,{x^2}\, + \,{y^2} + \,x\, - \,y\,\, = 0$

B.

$\,{x^2}\, + \,{y^2} - \,x\, + \,y\,\, = 0$

C.

$\,{x^2}\, + \,{y^2} + \,x\, + \,y\,\, = 0$

D.

$\,{x^2}\, + \,{y^2} - \,x\, - \,y\,\, = 0$

2004 Q180 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

If a circle passes through the point (a, b) and cuts the circle ${x^2}\, + \,{y^2} = 4$ orthogonally, then the locus of its centre is :

A.

$2ax\, - 2by\, - ({a^2}\, + \,{b^2} + 4) = 0$

B.

$2ax\, + 2by\, - ({a^2}\, + \,{b^2} + 4) = 0$

C.

$2ax\, - 2by\, + ({a^2}\, + \,{b^2} + 4) = 0$

D.

$2ax\, + 2by\, + ({a^2}\, + \,{b^2} + 4) = 0$

2004 Q181 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

If the lines 2x + 3y + 1 + 0 and 3x - y - 4 = 0 lie along diameter of a circle of circumference $10\,\pi $, then the equation of the circle is :

A.

${x^2}\, + \,{y^2} + \,2x\, - \,2y - \,23\,\, = 0$

B.

${x^2}\, + \,{y^2} - \,2x\, - \,2y - \,23\,\, = 0$

C.

${x^2}\, + \,{y^2} + \,2x\, + \,2y - \,23\,\, = 0$

D.

${x^2}\, + \,{y^2} - \,2x\, + \,2y - \,23\,\, = 0$

2003 Q182 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle having area as 154 sq. units. Then the equation of the circle is :

A.

${x^2}\, + \,{y^2} - \,2x\, + \,2y\,\, = \,62$

B.

${x^2}\, + \,{y^2} + \,2x\, - \,2y\,\, = \,62$

C.

${x^2}\, + \,{y^2} + \,2x\, - \,2y\,\, = \,47$

D.

${x^2}\, + \,{y^2} - \,2x\, + \,2y\,\, = \,47$

2003 Q183 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

If the two circles ${(x - 1)^2}\, + \,{(y - 3)^2} = \,{r^2}$ and $\,{x^2}\, + \,{y^2} - \,8x\, + \,2y\, + \,\,8\,\, = 0$ intersect in two distinct point, then :

A.

$r > 2$

B.

$2 < r < 8$

C.

$r < 2$

D.

$r = 2.$

2002 Q184 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

The centres of a set of circles, each of radius 3, lie on the circle ${x^2}\, + \,{y^2} = 25$. The locus of any point in the set is :

A.

$4\, \le \,\,{x^2}\, + \,{y^2}\, \le \,\,64$

B.

${x^2}\, + \,{y^2}\, \le \,\,25$

C.

${x^2}\, + \,{y^2}\, \ge \,\,25$

D.

$3\, \le \,\,{x^2}\, + \,{y^2}\, \le \,\,9$

2002 Q185 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

If the chord y = mx + 1 of the circle ${x^2}\, + \,{y^2} = 1$ subtends an angle of measure ${45^ \circ }$ at the major segment of the circle then value of m is :

A.

$2\, \pm \,\sqrt 2 \,\,$

B.

$ - \,2\, \pm \,\sqrt 2 \,$

C.

$- 1\, \pm \,\sqrt 2 \,\,$

D.

none of these

2002 Q186 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

The equation of a circle with origin as a center and passing through an equilateral triangle whose median is of length $3$$a$ is :

A.

${x^2}\, + \,{y^2} = 9{a^2}$

B.

${x^2}\, + \,{y^2} = 16{a^2}$

C.

${x^2}\, + \,{y^2} = 4{a^2}$

D.

${x^2}\, + \,{y^2} = {a^2}$

2002 Q187 JEE Mains MCQ

iCON Education HYD, 79930 92826, 73309 72826 14 Mar 2026

The centre of the circle passing through (0, 0) and (1, 0) and touching the circle ${x^2}\, + \,{y^2} = 9$ is :

A.

$\left( {{1 \over 2},\,{1 \over 2}} \right)$

B.

$\left( {{1 \over 2},\, - \,\sqrt 2 } \right)$

C.

$\left( {{3 \over 2},\,{1 \over 2}} \right)$

D.

$\left( {{1 \over 2},\,{3 \over 2}} \right)$

Mathematics Chapters

Circle

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation:

Explanation: