JEE MATHEMATICS MCQ: PARABOLA

1 Easy

1 of 1

Analyzing +4 | -1

Two parabolas

C

and

D

intersect at two different points, where

C

y=x^2-3

and

D

y=k x^2

. The intersection at which the

\mathrm{x}

value is positive is designated point

A

, and

x=a

at this intersection the tangent line

l

A

to the curve

D

intersects curve

C

at point

B

, other than

A

. If

x

-value of point

B

is 1 , then a is equal to

View answer and explanation

Correct option: C

Option C (3) is correct because solving the intersection of the two parabolas and the tangent line equation leads to a cubic equation with a root at a=3.

More Questions from PARABOLA

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The equation of a common tangent to the parabolas

y=x^2

and

y=-(x-2)^2

is A point

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

, is Let

P,Q,R

be three points on parabola

{y^2} = 4x

and normal at

P

and

R

meet at

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

is If

I

denotes the semi-latusrectum of the parabola

{y^2} = 4ax

and

SP

and

SQ

denote the segments of any focal chord

PQ,S

being the focus, then

SP,l

and

SQ

are in the relation