Problem

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 the focal chord and lines

QR

and

PK

are parallel, where

K

is the point

(2a, 0)

. The value of

r

is a.

-\frac{1}{t}

b.

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

c.

\frac{1}{t}

d.

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

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