Question

The focal distance of a point on the parabola $y^2=16x$ whose ordinate is twice the abscissa, is

• A. 6
• B. 8
• C. 10
• D. 12

Answer 1

The correct option is B 8

Let point be (h, k). But 2h = k, then $k^2=16h$
$\Rightarrow 4h^2=16h\Rightarrow h=0,h=4\Rightarrow k=0,k=8$
$\therefore$ Points are (0,0), (4,8).
Focal distance of any point (x,y) on the parabola $y^2=4ax$ is given by x+a.
Hence focal distances are 0 + a = 4, and 4 + 4 = 8