Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 51

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IMPORTANT

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The locus of a point from which tangents to a parabola are at right angles, is

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Important Questions on Parabola

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 52

P

is a point. Two tangents are drawn from it to the parabola

y^{2} = 4 x

such that the slope of one tangent is three times the slope of the other. The locus of

P

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 53

The locus of the middle points of chords of the parabola

y^{2} = 8 x

drawn through the vertex is a parabola whose

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 54

Circle drawn with diameter being any focal chord of the parabola

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

will always touch a fixed line, whose equation is

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

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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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

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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

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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

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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