Question

What is the focal distance of parabola $x^2=8y$ from the point $(4,2)$?

• A. 4

Answer 1

The correct option is A 4
The standard form
$x^2=4ay$ is similar to the given parabola $x^2=8y$ with value of $a$ as $2.$
Now, for parabola $x^2=4ay,$ the coordinates of focus is $(0,a).$
So, for $a=2,$ coordinates of focus is $(0,2).$

Also, the focal length at any given point on a parabola
$x^2=4ay$ is given as $y+a.$
Thus, at a given point $(4,2)$ the focal length would be $4.$ As, $y=2$ and $a=2.$