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JEE MATHEMATICS MCQ: PARABOLA

1 Easy

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Application +4 | -1

If the line

x + y - 1 = 0

is a tangent to the parabola

{y^2} - y + x = 0

, then the point of contact is

View answer and explanation

Correct option: A

\left( {0,1} \right)

Option A ((0,1)) is correct because it's the only point that satisfies both the line and parabola equations, indicating it's the point of contact.

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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