Question 1: Palette 1/9

BITSAT 2025 MCQ

The locus of the middle points of chords of the circle $x^2+y^2=25$ which are parallel to the line $x-2 y+3=0$ is

A

$x+2 y=0$

B

$2 x+y=0$

C

$x-2 y=0$

D

$2 x-y=0$

Question 2: Palette 2/9

BITSAT 2025 MCQ

What is the set of values of a for which the point ( $2 a, a+1$ ) is an interior point of the larger segment of the circle $x^2+y^2-2 x-2 y-8=0$ made by the chord $x-y+1=0$.

A

$\left(0, \frac{9}{5}\right)$

B

$(0, \infty)$

C

$\left(\frac{9}{5}, \infty\right)$

D

$(-\infty, 0)$

Question 3: Palette 3/9

BITSAT 2024 MCQ

The locus of the point of intersection of the lines $ x=a\left(\frac{1-t^{2}}{1+t^{2}}\right) $ and $ y=\frac{2 a t}{1+t^{2}} $ represent $ (t $ being a parameter)

A

Circle

B

Parabola

C

Ellipse

D

Hyperbola

Question 4: Palette 4/9

BITSAT 2024 MCQ

The locus of the mid-point of a chord of the circle $ x^{2}+y^{2}=4 $, which subtends a right angle at the origin is

A

$ x+y=2 $

B

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

C

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

D

$ x+y=1 $

Question 5: Palette 5/9

BITSAT 2023 MCQ

If the straight line $y=m x+c$, touches the circle $x^2+y^2=a^2$ at a point, then $c^2$ is

A

$m^2\left(1-a^2\right)$

B

$m^2\left(1+a^2\right)$

C

$a^2\left(1-m^2\right)$

D

$a^2\left(1+m^2\right)$

Question 6: Palette 6/9

BITSAT 2023 MCQ

A normal is drawn at the point $P$ to the circle $x^2+y^2=25$, which is inclined at $45^{\circ}$ with the straight line $y=6$. Then, the point lies on the straight line

A

$y=x$

B

$y=-x$

C

$y=\sqrt{3} x$

D

$\sqrt{3} y=x$

Question 7: Palette 7/9

BITSAT 2023 MCQ

If a tangent to the circle $x^2+y^2=1$ intersect the co-ordinate axes at distinct points $P$ and $Q$, then the locus of the mid-point of $P Q$ is

A

$x^2+y^2-2 x y=0$

B

$x^2+y^2-2 x^2 y^2=0$

C

$x^2+y^2-4 x^2 y^2=0$

D

$x^2+y^2-16 x^2 y^2=0$

Question 8: Palette 8/9

BITSAT 2022 MCQ

The locus of the mid-point of the chord if contact of tangents drawn from points lying on the straight line $4x - 5y = 20$ to the circle ${x^2} + {y^2} = 9$ is

A

$20({x^2} + {y^2}) - 36x + 45y = 0$

B

$20({x^2} + {y^2}) + 36x - 45y = 0$

C

$36({x^2} + {y^2}) - 20x + 45y = 0$

D

$36({x^2} + {y^2}) + 20x - 45y = 0$

Question 9: Palette 9/9

BITSAT 2021 MCQ

Equation of circle which passes through the points (1, $-$2) and (3, $-$4) and touch the X-axis is

A

x² + y² + 6x + 2y + 9 = 0

B

x² + y² + 10x + 20y + 25 = 0

C

x² + y² + 6x + 4y + 9 = 0

D

None of the above