Let , , , and be non-zero real numbers. Let , , , and be distinct points on the…

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Let

a

r

s

, and

t

be non-zero real numbers. Let

P(at^2,2at)

Q\left(\frac{a}{t^2},-\frac{2a}{t}\right)

R(ar^2,2ar)

, and

S(as^2,2as)

be distinct points on the parabola

y^2=4ax

. Suppose that

PQ

is a focal chord and lines

QR

and

PK

are parallel, where

K=(2a,0)

. The value of

r

is (1)

-\frac{1}{t}

(2)

\frac{t^2+1}{t}

(3)

\frac{1}{t}

(4)

\frac{t^2-1}{t}