← Back to Mathematics

Circle

178 Questions
All Exams JEE Mains JEE Advanced TS-EAMCET AP-EAPCET
2015 JEE Mains MCQ
JEE Main 2015 (Offline)
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 JEE Mains MCQ
JEE Main 2015 (Offline)
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 JEE Mains MCQ
JEE Main 2014 (Offline)
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 JEE Mains MCQ
JEE Main 2013 (Offline)
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 JEE Mains MCQ
AIEEE 2012
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 JEE Mains MCQ
AIEEE 2011
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 JEE Mains MCQ
AIEEE 2010
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 JEE Mains MCQ
AIEEE 2009
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 JEE Mains MCQ
AIEEE 2009
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 JEE Mains MCQ
AIEEE 2008
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 JEE Mains MCQ
AIEEE 2008
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 JEE Mains MCQ
AIEEE 2007
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 JEE Mains MCQ
AIEEE 2006
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 JEE Mains MCQ
AIEEE 2006
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 JEE Mains MCQ
AIEEE 2005
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 JEE Mains MCQ
AIEEE 2005
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 JEE Mains MCQ
AIEEE 2005
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 JEE Mains MCQ
AIEEE 2005
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 JEE Mains MCQ
AIEEE 2004
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 JEE Mains MCQ
AIEEE 2004
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 JEE Mains MCQ
AIEEE 2004
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 JEE Mains MCQ
AIEEE 2004
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 JEE Mains MCQ
AIEEE 2003
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 JEE Mains MCQ
AIEEE 2003
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 JEE Mains MCQ
AIEEE 2002
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 JEE Mains MCQ
AIEEE 2002
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 JEE Mains MCQ
AIEEE 2002
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 JEE Mains MCQ
AIEEE 2002
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.
$\left( {{1 \over 2},\,{3 \over 2}} \right)$