Question

Write the coordinates of the focus of parabola x² – 4x – 8y = 4.

Answer 1

Equation of parabola,

x² – 4x – 8y = 4

⇒ x² – 2.2x + (2)² = 8y + 4 + 2²

⇒ (x – 2)² = 8y + 8

= 8(y + 1)

(x-2)² = 4.2.(y + 1)

x² = 4.2.y

Where x = x – 2 and Y = y + 1

a = 2

Coordinates of focus = (0, a)

x = x- 2 = 0

⇒ x = 2

Y = y + 1 = 2

⇒ y = 1

Thus coordinates of focus = (2, 1)