Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 19

EASY

JEE Main

IMPORTANT

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The normal chord at a point $' t'$ on the parabola $16 y^{2} = x$ subtends a right angle at the vertex. Then $t$ is equal to

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Important Questions on Conic Section

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 20

The total number of chords that can be drawn from the point

(a, a)

to the circle

x^{2} + y^{2} = 2 a^{2}

such that they are bisected by the parabola

y^{2} = 4 a x,

is

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 21

Consider the parabola

3 y^{2} - 4 y - 6 x + 8 = 0 .

The points on the axis of this parabola from where

3

distinct normals can be drawn are given by

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 22

A (x_{1}, y_{1})

and

B (x_{2}, y_{2})

are any two points on the parabola

y = c x^{2} + b x + a .

If

P (x_{3}, y_{3})

be the point on the arc

AB

where the tangent is parallel to the chord

AB,

then

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 23

The locus of the point such that normals drawn at the point of contact of the tangents drawn from the point to the parabola, are such that the slope of one is double the slope of the other is

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 24

Number of the normals drawn from the point

(6, - 8)

to the parabola

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

is

HARD

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 25

Length of latusrectum of the parabola

25 [{(x - 1)}^{2} + {(y - 2)}^{2}] = {(3 x - 4 y + 8)}^{2}

is

EASY

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 26

The straight line

l x + m y + n = 0

will touch the parabola

y^{2} = 4 p x

if

MEDIUM

JEE Main

IMPORTANT

Eduwiser's Coordinate Geometry for JEE Main and Advanced>Chapter 7 - Conic Section>7.1>Q 27

The two parabolas

y^{2} = 4 a x

and

y^{2} = 4 c (x - b)

cannot have a common normal other than the axis, unless