1
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

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
$$a^2\left(1+m^2\right)$$
2
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

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
$$\sqrt{3} y=x$$
3
BITSAT 2023
MCQ (Single Correct Answer)
+3
-1

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
$$x^2+y^2-16 x^2 y^2=0$$
4
BITSAT 2022
MCQ (Single Correct Answer)
+3
-1

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