Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 55

MEDIUM

JEE Advanced

IMPORTANT

Earn 100

Tangents are drawn to $y^{2} = 4 a x$ from the points, where the line $l x + m y + n = 0$ meets the parabola. Point of intersection of these tangents is

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Important Questions on Parabola

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 56

Locus of mid-point of chords of the parabola

y^{2} = 4 a x

that pass through the point

(3 a, a)

is

MEDIUM

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 57

If straight lines

(y - b) = m_{1} (x + a)

and

(y - b) = m_{2} (x + a)

are the tangents of

y^{2} = 4 a x,

then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 58

Tangents drawn to parabola

y^{2} = 4 a x

at the points

A

and

B

intersect at

C .

If

S

is the focus of the parabola, then

S A, S C

and

S B

forms

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 59

If the line

a x + b y + c = 0

is a tangent to the parabola

y^{2} - 4 y - 8 x + 32 = 0

, then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 60

If the tangent drawn from a point to the parabola

y^{2} = 4 a x

are normals to the parabola

x^{2} = 4 b y,

then

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 61

If mutually perpendicular tangents

T A

and

T B

are drawn to

y^{2} = 4 a x,

then minimum length of

A B

is equal to

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 62

P A

and

P B

are tangents drawn to

y^{2} = 4 a x

from arbitrary point

P .

If the angle between tangents is

\frac{π}{4},

then locus of the point

P

is

HARD

JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 63

P A

and

P B

are the tangents drawn to

y^{2} = 4 a x

from point

P .

These tangents meet

Y

-axis at the points

A_{1}

and

B_{1},

respectively. If the area of

Δ P A_{1} B_{1}

is

2

sq. units, then locus of

P

is