Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 8

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IMPORTANT

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If the normal to a parabola $y^{2} = 4 a x$ at $P$ meets the curve again in $Q$ and if $P Q$ and the normal at $Q$ makes angle $α$ and $β,$

respectively, with the $x$ -axis, then $\tan α (\tan α + \tan β)$ has the value equal to

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Important Questions on Parabola

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 9

A line is a common tangent to the circle

{(x - 3)}^{2} + y^{2} = 9

and the parabola

y^{2} = 4 x

. If the two points of contact

(a, b)

and

(c, d)

are distinct and lie in the first quadrant, then

2 (a + c)

is equal to ___ .

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Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 10

Let

P, Q

be the points with parameters

t_{1}, t_{2}

on the parabola

y^{2} = 4 a x .

If the normals at

P, Q

meet on the parabola at

R (t_{3}),

then

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Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 11

The equation of common normal to the circle

x^{2} + y^{2} - 12 x + 16 = 0

and parabola

y^{2} = 4 x

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 12

Normals at

A, B, C

are drawn to

y^{2} = 4 x

which intersects at

P (3, 0)

. Then the equation of circumcircle of

Δ A B C

is

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Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 13

If

L

is the minimum distance between the curves

{(x - 6)}^{2} + y^{2} = 5

and

y^{2} = 4 x

, then the value of

L^{2}

is

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Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 14

The number of points with integral coordinates that lie in the interior of the region common to the circle

x^{2} + y^{2} = 16

and the parabola

y^{2} = 4 x

is

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JEE Main

IMPORTANT

Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 2>Q 15

A tangent and normal is drawn at the point

P \equiv (16, 16)

of the parabola

y^{2} = 16 x

which cut the axis of the parabola at the points

A

and

B,

respectively. If the centre of the circle through

P,

A

and

B

is

C

, then the angle between

P C

and the axis of

x

is

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IMPORTANT

Mathematics Crash Course JEE Main>Chapter 20 - Parabola>Level 3>Q 1

The tangent and normal at the point

P (a t^{2}, 2 a t)

to the parabola

y^{2} = 4 a x

meet the

x

-axis in

T

and

G,

respectively, then the angle at which the tangent at

P

to the parabola is inclined to the tangent at

P

to the circle through

P, T, G

is