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JEE MATHEMATICS MCQ: PARABOLA

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Analyzing +4 | -1

Let

A, B

, and

C

be three points taken on the parabola

y^2=4 a x

with coordinates

\left(a t_i{ }^2, 2 a t_i\right) ; i=1,2,3

; where

t_1, t_2

and,

t_3

are in A.P. If

A A^{\prime}, B B^{\prime}

and

C C^{\prime}

are focal chords and coordinates of

A^{\prime}, B^{\prime}

and

C^{\prime}

are

\left(a t_i^{\prime^2}, 2 a t_i^{\prime}\right) ; i=1,2,3

; then

t^{\prime}{ }_1, t^{\prime}{ }_2

and

t^{\prime}{ }_3

are in

View answer and explanation

Correct option: C

HP

Option C (HP) is correct because if

t_1, t_2, t_3

are in AP, then

t'_1, t'_2, t'_3

are in HP, where

t'_i = -1/t_i

.

More Questions from PARABOLA

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The equation of a common tangent to the parabolas

y=x^2

y=-(x-2)^2

P

moves such that slope of one tangent drawn from it to parabola

y^2=16 x

is four times the slope of other tangent, then the length of latus rectum of the conic represented by locus of

P

P,Q,R

be three points on parabola

{y^2} = 4x

P

R

Q

, then the locus of the mid-point of the chord

PR

is a parabola whose vertex is at The tangents at the end points of any chord through

(1,0)

to the parabola

y^2+4 x=8

intersect The focus of the parabola

x^2=-16 y

I

denotes the semi-latusrectum of the parabola

{y^2} = 4ax

SP

SQ

denote the segments of any focal chord

PQ,S

being the focus, then

SP,l

SQ

are in the relation