Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 30

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JEE Advanced

IMPORTANT

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Tangent at the vertex of a parabola divides the distance between directrix and latus rectum in the ratio

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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 31

The chord

A B

of the parabola

y^{2} = 4 a x

cuts the axis of the parabola at

C .

If

A = (a t_{1}^{2}, 2 a t_{1}), B = (a t_{2}^{2}, 2 a t_{2})

and

A C : A B = 1 : 3,

then

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 32

A B

is a chord of the parabola

y^{2} = 4 a x .

If its equation is

y = m x + c

and it subtends a right angle at the vertex of the parabola, then

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 33

Locus of trisection point of any double ordinate of

y^{2} = 4 a x

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 34

Circle drawn having its diameter equal to focal distance of any point lying on the parabola

x^{2} - 4 x + 6 y + 10 = 0,

will 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 35

An equilateral

Δ S A B

is inscribed in the parabola

y^{2} = 4 a x

having its focus at

S .

If chord

A B

lies towards the left of

S,

then side length of this triangle is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 36

Normals

A O, A A_{1}, A A_{2}

are drawn to the parabola

y^{2} = 8 x

from the point

A (h, 0) .

If

Δ O A_{1} A_{2}

is equilateral, then the possible values of

h

is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 37

The locus of centre of a circle that passes through

P (a, b)

and touch the line

y = m x + c

(it is given that,

b \neq m a + c

) is

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JEE Advanced

IMPORTANT

Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 38

The parabola

y^{2} = 4 x

and the circle

{(x - 6)}^{2} + y^{2} = r^{2}

will have no common tangent, if