Question

On the parabola $y^2=8x$ if one extremity of a focal chord is $\left(\frac{1}{2},-2\right)$ then its other extremity is

• A. $(2,2)$
• B. $\left(\frac{1}{8},-8\right)$
• C. $(8,\frac{1}{8})$
• D. $(8,8)$

Answer 1

Answer: (D)

$(8,8)$

For $(\frac{1}{2},-2)$, $t=\frac{-1}{2}$

Let the other extremity be $t_2$

Then $t{t}_2=-1$ .....(property of focal chord)

$\Rightarrow t_2=2$

Therefore, $(a{t}_2^2,2a{t}_2)=(8,8)$