EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 10 - Parabola>TS EAMCET 2021 (04-Aug Shift-1)>Q 3

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A point on the parabola whose focus and vertex are respectively at $(\frac{5}{4}, - 2)$ and $(1, - 2)$ is

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Important Questions on Parabola

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 10 - Parabola>TS EAMCET 2021 (04-Aug Shift-1)>Q 4

The parametric equations of the parabola

y^{2} - 4 x - 8 y - 12 = 0

are

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 10 - Parabola>TS EAMCET 2021 (04-Aug Shift-2)>Q 5

Match the items given in List-A with those of the items of List-B

	List-A		List-B
(A)	The vertex of the parabola $y^{2} + 4 x - 2 y + 3 = 0$ is	(I)	$(\frac{5}{4}, 1)$
(B)	The vertex of the parabola $x^{2} + 8 x + 12 y + 4 = 0$ is	(II)	$(1, \frac{5}{4})$
(C)	The focus of the parabola $y^{2} - x - 2 y + 2 = 0$ is	(III)	$(\frac{- 1}{2}, 1)$
(D)	The focus of the parabola $x^{2} - 2 x - 8 y - 23 = 0$ is	(IV)	$(1, - 1)$
		(V)	$(- 4, 1)$

The correct match is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 10 - Parabola>TS EAMCET 2021 (04-Aug Shift-2)>Q 6

For the parabola

y = 2 + 4 t, x = - 2 + 2 t^{2}

the ends of the latus rectum are at

t = α

and

t = β

, then

α β =

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 10 - Parabola>TS EAMCET - 5 August 2021 Shift 2>Q 7

The parametric equations of the parabola

x^{2} - 8 x + 12 y + 15 = 0

are

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 10 - Parabola>TS EAMCET - 5 August 2021 Shift 2>Q 8

The equation of the directrix of the parabola

(2 x - 3 y - 5)^{2} = 20 (3 x + 2 y + 1)

is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 10 - Parabola>TS EAMCET 2020 (9-Sep Shift-1)>Q 9

If

x - 2 y + k = 0

is a tangent to the parabola

y^{2} - 4 x - 4 y + 8 = 0,

then the slope of the tangent drawn at

(1, k)

on the given parabola is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 10 - Parabola>TS EAMCET 2020 (9-Sep Shift-1)>Q 10

The number of points on the parabola

y^{2} = x

at which the slope of the normal drawn at the point is equal to the

x

-coordinate of that point is

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EMBIBE CHAPTER WISE PREVIOUS YEAR PAPERS FOR MATHEMATICS>Chapter 10 - Parabola>TS EAMCET 2018 (04-May Shift-1)>Q 11

If two tangents to the parabola

y^{2} = 8 x

meet the tangent at its vertex in

M

and

N

such that

M N = 4

, then the locus of the point of intersection of those two tangents is