JEE MATHEMATICS MCQ: PARABOLA

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The set of points

(x, y)

whose distance from the line

y=2 x+2

is the same as the distance from

(2,0)

is a parabola. This parabola is congruent to the parabola in standard from

y=k x^2

for some

k

which is equal to

View answer and explanation

Correct option: D

\frac{\sqrt{5}}{12}

Option D (

\frac{\sqrt{5}}{12}

) is correct because equating the distance from a point to a line and a fixed point results in a parabola, and transforming it to standard form reveals k =

\frac{\sqrt{5}}{12}

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