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Parabola
Practice Questions
MCQ (Single Correct Answer)
1

If $P$ is a point which divides the line segment joining the focus of the parabola $y^2=12 x$ and a point on the parabola in the ratio $1: 2$. Then, the locus of $p$ is

AP EAPCET 2024 - 23th May Morning Shift
2
Equation of the line touching both parabolas $y^2=4 x$ and $x^2=-32 y$ is
AP EAPCET 2024 - 22th May Evening Shift
3
If the normal chord drawn at $(2 a, 2 a \sqrt{2})$ on the parabola $y^2=4 a x$ subtends an angle $\theta$ at its vertex, then $\theta=$
AP EAPCET 2024 - 22th May Morning Shift
4
If the ordinates of points $P$ and $Q$ on the parabola $y^2=12 x$ are in the ratio $1: 2$. Then, the locus of the point of intersection of the normals to the parabola at $P$ and $Q$ is
AP EAPCET 2024 - 21th May Evening Shift
5
A common tangent to the circle $x^2+y^2=9$ and parabola $y^2=8 x$ is
AP EAPCET 2024 - 20th May Morning Shift
6
The normal drawn at a point $(2,-4)$ on the parabola $y^2 \pm 8 x$ cuts again the same parabola at $(\alpha, \beta)$, then $\alpha+\beta=$
AP EAPCET 2024 - 19th May Evening Shift
7
If the axes are rotated through an angle $45^{\circ}$ about the origin in anticlockwise direction, then the transformed equation of $y^2=4 a r$ is
AP EAPCET 2024 - 18th May Morning Shift
8
The line $x-2 y-3=0$ cuts the parabola $y^2=4 \operatorname{ar}$ at the points $P$ and $Q$. If the focus of this parabola is $\left(\frac{1}{4}, k\right)$. then $P Q=$
AP EAPCET 2024 - 18th May Morning Shift
9

Which of the following represents a parabola?

AP EAPCET 2022 - 5th July Morning Shift
10

Suppose a parabola passes through $$(0,4),(1,9)$$ and $$(4,5)$$ and has its axis parallel to the $$Y$$-axis. Then, the equation of the parabola is

AP EAPCET 2022 - 4th July Evening Shift
11

Suppose a parabola with focus at $$(0,0)$$ has $$x-y+1=0$$ as its tangent at the vertex. Then, the equation of its directrix is

AP EAPCET 2022 - 4th July Morning Shift
12

If $$a x+b y=1$$ is a normal to the parabola $$y^2=4 p x$$, then the condition is

AP EAPCET 2022 - 4th July Morning Shift
13

The coordinates of the focus of the parabola described parametrically by $$x=5t^2+2$$ and $$y=10t+4$$ (where t is a parameter) are

AP EAPCET 2021 - 20th August Morning Shift
14

Find the equation of the parabola which passes through (6, $$-$$2), has its vertex at the origin and its axis along the Y-axis.

AP EAPCET 2021 - 19th August Evening Shift
15

If one end of focal chord of the parabola $$y^2=8x$$ is $$\left(\frac{1}{2},2\right)$$, then the length of the focal chord is ................ units.

AP EAPCET 2021 - 19th August Morning Shift