Discussion Forum

The focus of the curve y² + 4x- 6y + 13 = 0 is

Answer:

Explanation:

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).