JEE MATHEMATICS MCQ: PARABOLA

1 Easy

1 of 1

Analyzing +4 | -1

Let

x = 2t,\,\,y = \frac{{{t^2}}}{3}

be a conic. Let

S

be the focus and

B

be the point on the axis of the conic such that

SA \bot BA

where

A

is any point on the conic. If

k

is the ordinate of the centroid of the

\Delta SAB,

then

\lim\limits_{t \to 1} k\,

is equal to

View answer and explanation

Correct option: D

\frac{{13}}{{18}}

The correct answer is D (

\frac{{13}}{{18}}

) because it is the limit of the ordinate of the centroid of the triangle SAB as t approaches 1, calculated using the properties of the conic and the given geometric conditions.

More Questions from PARABOLA

Practice All Chapter MCQs →

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