JEE MATHEMATICS MCQ: PARABOLA

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The locus of the middle points of the chords of the parabola

y^2=4 a x

which pass through the focus, is

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Correct option: C

y^2-2 a x+2 a^2=0

Option C (

y^2-2 a x+2 a^2=0

) is correct because it is the locus of the midpoints of the chords of the parabola that pass through the focus, found by using the equation T = S' and the condition that the chord passes through the focus.

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