Question

Find the coordinates of a point on the parabola y2 = 8x whose focal distance is 4.

Answer 1

We know that equation of an ellipse is y² = 4ax,

Also we have length of latus rectum = 4a

Now by comparing the above two equations,

4a = 8

Therefore

a = 2

y² = 8 × 2 = 16

y = ± 4 and x = 2

Hence the co – ordinates are (2, 4) and (2, -4).