Question

Find the vertex, focus, equation of directrix and length of the latus rectum of the following:

y² – 4y – 8x + 12 = 0

Answer 1

y² – 4y = 8x – 12

(y – 2)² = 8x – 12 + 4

= 8x – 8

= 8(x – 1)

(y – 2)² = 8(x – 1)

It is form of (y – k)² = Aa(x – h)

4a = 8

⇒ a = 2

(a) Vertex (h, k) = (1, 2)

(b) Focus = (a + h, 0 + k)

= (2 + 1, 0 + 2)

= (3, 2)

(c) Equation of the directrix x = – a + h

= – 2 + 1

= – 1

x + 1 = 0

(d) Length of latus rectum is

4a = 4 × 2

= 8 units.