VITEEE 2018 Paper

The given equation of curve is:
y2 + 4x- 6y + 13 = 0
which can be written as:
y2 - 6y + 9 + 4x + 4 = 0
⇒ (y2 - 6y + 9) = -4(x + 1)
⇒ (y−3)2 = -4(x + 1)
Put Y = y - 3 and X = x + 1
On comparing Y2 = 4aX
Length of focus from vertex,
a = - 1
At focus X = a and Y = 0
⇒ x + 1 = - 1
⇒ x = - 2∴. y-3 = 0 ⇒ y=3
∴ Focus is (- 2, 3).