Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice II>Q 10

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Let there be 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 the middle points of the intercepts between the parabolas made on the lines parallel to the common axis is a

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Important Questions on Parabola

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JEE Main/Advanced

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>Multiple Choice II>Q 11

A chord

P P'

of a parabola cuts the axis of the parabola at

O

. The feet of the perpendiculars from

P

and

P'

on the axis are

M

and

M'

respectively. If

V

is the vertex then

V M, V O, V M'

are in:

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>FILL IN THE BLANKS>Q 1

Two tangents are drawn from the point

(- 2, - 1)

to the parabola

y^{2} = 4 x

. If

θ

is the angle between these tangents, then

\tan θ =

____

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>FILL IN THE BLANKS>Q 2

The length of the Latus rectum of the parabola

x = a y^{2} + b y + c

is _____

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>FILL IN THE BLANKS>Q 3

If

y + b = m_{1} (x + a)

and

y + b = m_{2} (x + a)

are two tangents of the parabola

y^{2} = 4 a x

then

m_{1} m_{2}

is equal to _____ .

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>FILL IN THE BLANKS>Q 4

The subtangent, ordinate and subnormal to the parabola

y^{2} = 4 a x

at a point (different from the origin) are in

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>FILL IN THE BLANKS>Q 5

If the polar of a point with respect to the circle

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

Touches the parabola

y^{2} = 4 a x

, then the locus of the pole is ______

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>FILL IN THE BLANKS>Q 6

The orthocentre of a triangle formed by any three tangents to a parabola lies on _____.

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Skills in Mathematics Coordinate Geometry for JEE Main & Advanced>Chapter 5 - Parabola>FILL IN THE BLANKS>Q 7

If the normal at

P (t)

on

y^{2} = 4 a x

meets the curve again at

Q

, the point

R

on the curve, the normal at which also passes through

Q

has co-ordinates

(__)