# Psq is a Focal Chord of the Parabola Y2 = 8x. If Sp = 6, Then Write Sq. - Mathematics

PSQ is a focal chord of the parabola y2 = 8x. If SP = 6, then write SQ

#### Solution

The coordinates of the focal chord are $P \left( a t^2 , 2at \right) a\text{ and } Q \left( \frac{a}{t^2}, \frac{- 2a}{t} \right)$

Comparing y2 = 8x with

$y^2 = 4ax$
a = 2
Therefore, the coordinates of the focus S is $\left( 2, 0 \right)$
Given:
SP = 6
$\therefore \sqrt{\left( 2 - 2 t^2 \right)^2 + \left( 4t \right)^2} = 6$
$\Rightarrow t^4 + 2 t^2 - 8 = 0$
$\Rightarrow t^2 = 2$

Thus, we have:
SQ = $\sqrt{\left( 2 - \frac{2}{t^2} \right)^2 + \left( \frac{4}{t^2} \right)}$

$\sqrt{\left( 2 - \frac{2}{2} \right)^2 + \left( \frac{4}{2} \right)}$

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 25 Parabola
Exercise 25.2 | Q 7 | Page 28