Question

What is the focus of the parabola `y^2+6y+8x+25 = 0`?

Answer 1

`( -4, -3 )`

Explanation:

Focus of the parabola `(y-b)^2 = 4 k ( x-a) is (a +-k, b)`
The given equation is `( y + 3 )^2 = -8 ( x + 2 )`
Here, a = `-`2, b = `-`3 and k = `-`2.
The vertex of the parabola is at `(-2, -3 )`.
The focus is (a + k, b ) = (`-`4, `-`3 )
The axis is in the negative x-direction..