Question

The coordinates of the end-points of the latusrectum of the parabola x² + 8y = 0 are __________.

Answer 1

Given parabola is x² + 8y = 0
i.e. x² = −4(2)y
i.e. a = 2
∴ Focus point is (0, −2)

Let us suppose co-ordinate of P be (p, 2) and Q be (p, −2)
Since both points P and Q lie an x² = −8y
i.e. p² = − 8 (−2) for (p, −2)
i.e. p² = 16
i.e. p = ± 4
∴ co-ordinate of P are (4, −2) and Q are (−4, −2)