Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 1>Q 15

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IMPORTANT

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If two of the normal of the parabola $y^{2} = 4 x$ that passes through $(15, 12)$ are $4 x + y = 72$ and $3 x - y = 33$ , then the third normal is

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Important Questions on Parabola

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 1>Q 16

If

2 x + 3 y = α, x - y = β

and

k x + 15 y = r

are

3

concurrent normals of parabola

y^{2} = λ x

, then the value of

k

is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 1>Q 17

Length of the normal chord of parabola

y^{2} = 4 x

which makes an angle of

\frac{π}{4}

with the axis of

x

is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 1>Q 18

Locus of the intersection of the tangents at the ends of the normal chords of the parabola

y^{2} = 4 a x

is -

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Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 1

If

a x^{2} + 2 h x y + b y^{2} - 82 x + 98 y + 144 = 0

is the equation of a parabola with focus

(2, - 3)

and directrix

3 x - 2 y + 5 = 0,

then

a x^{2} + 2 h x y + b y^{2} = 0

represents

HARD

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 2

The shortest distance between the line

x - y = 1

and the curve

x^{2} = 2 y

is:

HARD

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 3

The equation of one of the common tangents to the parabola

y^{2} = 8 x

and

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

is

HARD

JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 4

Two tangents are drawn from

(p, q)

to the parabola

y^{2} = 8 x

such that the slope of one of the tangent is thrice of the other, then

\frac{3 q^{2}}{p} =

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 5

A line

y = \sqrt{3} x + λ

is drawn through focus

S

of the parabola

y^{2} = 8 x + 16

. If two intersection points of the given line and the parabola are

A

and

B

such that perpendicular bisector of

A B

intersects the

x

-axis at

P

then the length of

P S

is