Question

Coordinates of a point on the parabola $y^2$ = $8x$ whose focal distance is 4 , are

• A. $(\frac{1}{2},2)$
• B. $(1,\pm 2\sqrt{2})$
• C. $(2,\pm 4)$
• D. None of these

Answer 1

The correct option is C $(2,\pm 4)$

Given,

$y^2=8x$

$\Rightarrow y^2=4\left(2\right)x$

Focus $(2,0)$

Let $P(x_1,y_1)$ be a point on parabola.

$\Rightarrow \sqrt{(x_1-2{)}^2+y_1^2}=4$

$(x_1-2{)}^2+y_1^2=16$

$x_1^2+4-4x_1+\left(8x_1\right)=16$

$(x_1-2)(x_1+6)=0$

$\therefore x_1=2,-6$

as $x_1>0$

$\therefore x_1=2\Rightarrow y_1=8x_1=8\left(2\right)=16$

$\therefore y_1=\pm 4$

Points are $(2,\pm 4)$