Question
Question: The equation of the parabola whose vertex is at (2, -1) and focus at (2, -3) is...
The equation of the parabola whose vertex is at (2, -1) and focus at (2, -3) is
A
x2 + 4x – 8y – 12 = 0
B
x2 – 4x + 8y + 12 =0
C
x2 + 8y = 12
D
x2 – 4x + 12 =0
Answer
x2 – 4x + 8y + 12 =0
Explanation
Solution
VS =(2−2)2+(−3+1)2=2. From (x-h)2 = -4a(y-k)
Parabola is
(x – 2)2 = -4.2(y+1)
⇒ (x – 2)2 = -8(y+1)
⇒ x2 + 4 – 4x = -8y – 8
⇒ x2 – 4x + 8y + 12 = 0