Question

The focal distance of a point on the parabola $y^2=8x$ is $10.$ Its coordinates are

• A. $(2,\pm 2)$
• B. $(3,\pm 3)$
• C. $(5,\pm 5)$
• D. $(8,\pm 8)$

Answer 1

The correct option is D $(8,\pm 8)$

The equation of parabola is

$y^2=8x$

$\Rightarrow$ $4a=8$

$\therefore$ $a=2$

Then the co-ordinates of focus $S$ is $(2,0).$

Given focal distance is $10.$

$\Rightarrow$ $x+2=10$

$\Rightarrow$ $x=8$

$\Rightarrow$ $y^2=8x$

$\Rightarrow$ $y^2=8\left(8\right)$

$\Rightarrow$ $y^2=64$

$\therefore$ $y=\pm 8$

Hence, the co-ordinates are $(8,\pm 8)$