The focus of parabola x2 – 4x + 2y + 8 = 0 is | MATH - PARABOLA | SolveeIt | Solveeit

Today, August 19

Question

The focus of parabola x² – 4x + 2y + 8 = 0 is

A

(3/2, –2)

B

(5/2, –2)

C

(2, –3/2)

D

(2, –5/2)

Answer

(2, –5/2)

Explanation

Solution

x² – 4x + 2y + 8 = 0

x² – 4x + 4 = – 2y – 8 + 4

(x – 2)² = – 2y – 4

̃ (x – 2)² = – 2(y + 2) ̃ X² = – 2Y

Focus

X = 0, Y = –1/2

x – 2 = 0, y + 2 = –1/2

x = 2, y = – 5/2

(2, –5/2)