Question

For the parabola $y^2=4x,$ the point $p$ whose focal distance is $17$ is

• A. $(16,8)$ or $(16,-8)$
• B. $(8,8)$ or $8,-8)$
• C. $(4,8)$ or $(4,-8)$
• D. None of these

Answer 1

The correct option is A $(16,8)$ or $(16,-8)$

Let $P(x_1,y_1)$ be the point.

Since parabola is $y^2=4x,$

$\therefore 4a=4\Rightarrow a=1$

$\therefore$ Focal distance $=17$

$x_1+a=17\Rightarrow x_1+1=17\Rightarrow x_1=16$

$\therefore y_1^2=4x_1=4\left(16\right)=64$

$\therefore y_1=\pm 8$

$\therefore P$ is $(16,8)$ or, $(16,-8)$