Question

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

Answer 1

Given parabola is y² = 8x  ......(i)

Comparing with the equation of parabola y² = 4ax

4a = 8

⇒ a = 2

Now focal distance = |x + a|

⇒ |x + a| = 4

⇒ (x + a) = ± 4

⇒ x + 2 = ± 4

⇒ x = 4 – 2 = 2

And x = – 6

But x ≠ – 6

∴ x = 2

Put x = 2 in equation (i) we get

y² = 8 × 2 = 16

∴ y = ± 4

So, the coordinates of the point are (2, 4), (2, – 4).

Hence, the required coordinates are (2, 4) and (2, – 4).