Question

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

• A. $(2,-4)$
• B. $(\frac{1}{2},-2)$
• C. $(\frac{1}{2},2)$
• D. $(2,4)$

Answer 1

Answer: (A), (D)

The correct options are
A $(2,-4)$
D $(2,4)$

Let the point on the parabola $y^2=8x$ be $P(x,y).$
Then its focal distance is $SP=x+a$.
Here, $a=2\text{and}SP=4.$
$\therefore 4=x+2$
$\Rightarrow x=2$
$\Rightarrow y^2=8\times 2$
$\Rightarrow y=\pm 4$
Thus, the coordinates of the required points are $(2\pm 4)$.