Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Work Book Exercise 14.3>Q 2

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The inclination of the normal with positive direction of $X$ -axis, drawn at another end of a normal to the parabola $y^{2} = 4 x$ is always

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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>Work Book Exercise 14.3>Q 3

Two parabolas with the same axis, focus of each being exterior to the other and the latus rectum being

4 a

and

4 b

. The locus of middle points of the intercepts between the parabolas made on the lines parallel to the common axis is a/an

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Work Book Exercise 14.3>Q 4

The set of real values of

a

for which at least one tangent to

y^{2} = 4 a x

becomes normal to the circle

x^{2} + y^{2} - 2 a x - 4 a y + 3 a^{2} = 0

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Work Book Exercise 14.3>Q 5

If

P

,

Q

and

R

are three points on parabola

y^{2} = 4 x

and normal at

P

and

R

meet at

Q

, then the locus of midpoint of the chord

P R

is a parabola whose vertex is at

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JEE Advanced

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Work Book Exercise 14.3>Q 7

If

(x_{1}, y_{1}), (x_{2}, y_{2})

and

(x_{3}, y_{3})

are the feet of the three normals drawn from a point to the parabola

y^{2} = 4 a x,

then

\frac{x_{1} - x_{2}}{y_{3}} + \frac{x_{2} - x_{3}}{y_{1}} + \frac{x_{3} - x_{1}}{y_{2}}

is equal to

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

Equation of parabola having the extremities of its latus rectum as

(3, 4)

and

(4, 3)

is

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 2

The length of the latus rectum of the parabola

2 \{{(x - a)}^{2} + {(y - a)}^{2}\} = {(x + y)}^{2}

is

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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 3

Double ordinate

A B

of the parabola

y^{2} = 4 a x

subtends an angle

\frac{π}{2}

at the vertex of the parabola, then tangents drawn to parabola at

A

and

B

will intersect at

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Complete Study Pack for Engineering Entrances Objective Mathematics Vol 1>Chapter 14 - Parabola>Target Exercises>Q 4

A B

is a focal chord of

x^{2} - 2 x + y - 2 = 0,

whose focus is

S .

If

A S = l_{1},

then

B S

is equal to