Question

If $(2,-8)$ is one end of focal chord of the parabola $y^2=32x$, then the other end of the focal chord, is

• A. $(32,32)$
• B. $(32,-32)$
• C. $(-2,8)$
• D. $(2,8)$

Answer 1

The correct option is A $(32,32)$

Solution:- (A) $(32,32)$

As we know that if $(x_1,y_1)$ and $(x_2,y_2)$ are two ends of focal chord of parabola $y^2=4ax$, then

$x_1.x_2=a^2$

Given equation of parabola-

$y^2=32x$

Vertex of parabola $\equiv (0,0)$

$\therefore a=8$

One end of the chord $=(2,-8)$

Let the other end of the chod be $(x,y)$.

$\therefore 2x=8^2$

$\Rightarrow x=32$

Substituting the value of $x$ in the given equation of the parabola, we have

$y^2=32\times 32$

$y=\pm 32$

As the one end of the focal chord is on $(2,-8)$ hence the other end of the chord will be $(32,32)$.