Question

The focus of the parabola x² – 8x + 2y + 7 = 0 is ........

(a) [4, (9/2)]

(b) [0, (1/2)]

(c) [4, (9/2)]

(d) (4, 4)

Answer 1

The correct option (c) [4, (9/2)]   

Explanation:

Parabola is x² – 8x + 2y + 7 = 0

∴   (x – 4)² = – 2y – 7 + 16

∴   (x – 4)² = – 2[y – (9/2)]

∴   x² = – 4ay  

⇒ x = x – 4, y = y – (9/2) and 2 = 4a i.e. a = (1/2) 

Its focus is given by x = 0 and y = 0

i.e. x – 4 = 0   and     y – (9/3) = 0

∴    x = 4    and y = (9/2)

∴ focus [4, (9/2)].