Question

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

x² – 2x + 8y + 17 = 0

Answer 1

x² – 2x = -8y – 17

(x – 1)² = – 8y – 17 + 1

(x – 1)² = – 8y – 16

(x – 1)² = – 8(y + 2)

It is form of (x – h)² = – 4a(y – k)

4a = 8

⇒ a = 2

(a) Vertex be (h, k) = (1, – 2)

(b) Foeus = (0 + h, – a + k)

= (0 + 1, – 2 – 2)

= (1, – 4)

(c) Equation of the directrix is y + k + a = 0

y – 2 + 2 = 0

y = 0

(d) Length of latus rectum is 4a

= 4 × 2

= 8 units