Parabola · Mathematics · AP EAPCET

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MCQ (Single Correct Answer)

1
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
2
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
3
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
4
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
5

Which of the following represents a parabola?

AP EAPCET 2022 - 5th July Morning Shift
6

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
7

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
8

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
9

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
10

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
11

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
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