Question

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

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

Answer 1

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

Given,

$y^2=32x$

$\Rightarrow 4a=32$

$\therefore a=8$

Now,

$(2,8)\equiv (a{t}_1^2,2a{t}_1)$

$a{t}_1^2=2$

$8t_1^2=2$

$t_1^2=\frac{1}{4}$

$8=2\left(8\right)t_1$

$t_1=\frac{1}{2}$

$\Rightarrow t_2=-2$

Now,

$(a{t}_2^2,2a{t}_2)$

$=8\times (-2{)}^2,2\times 8\times (-2)$

$=(32,32)$