Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>FILL IN THE BLANKS>Q 16

HARD

JEE Main/Advanced

IMPORTANT

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The condition that the parabola $y^{2} = 4 c (x - d)$ and $y^{2} = 4 a x$ have a common normal other than $x$ -axis $(a > 0, c > 0),$ if $d + 2 c >$

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Important Questions on Parabola

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>INTRODUCTORY EXERCISE 5.1>Q 1

The vertex of the parabola

y^{2} + 6 x - 2 y + 13 = 0

is :

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>INTRODUCTORY EXERCISE 5.1>Q 2

If the parabola

y^{2} = 4 a x

passes through

(- 3, 2)

, then length of its latus rectum is

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>INTRODUCTORY EXERCISE 5.1>Q 3

The value of

p

such that the vertex of

y = x^{2} + 2 p x + 13

is 4 units above the

x

-axis is :

HARD

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>INTRODUCTORY EXERCISE 5.1>Q 4

The length of the latusrectum of the parabola whose focus is

(3,3)

and directrix is

3 x - 4 y - 2 = 0,

is

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>INTRODUCTORY EXERCISE 5.1>Q 5

If the vertex and focus of a parabola are

(3, 3)

and

(- 3, 3)

respectively, then its equation is :

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>INTRODUCTORY EXERCISE 5.1>Q 6

If the vertex of the parabola

y = x^{2} - 8 x + c

lies on

X -

axis, then the value of

c

is

EASY

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>INTRODUCTORY EXERCISE 5.1>Q 7

The parabola having its focus at

(3, 2)

and directrix along the

y

-axis has its vertex at

MEDIUM

JEE Main/Advanced

IMPORTANT

Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>INTRODUCTORY EXERCISE 5.1>Q 8

The directrix of the parabola

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

is