write the distance between the vertex and focus of the parabola y2 + 6y + 2x + 5 = 0
Given equation of the parabola is y2 + 6y + 2x + 5 = 0
⇒ y2 + 6y + 5 = - 2x
⇒ y2 + 6y + 9 = - 2x + 4
⇒ (y + 3)2 = - 2(x - 2)
Comparing with standard form of parabola (y - a)2 = - 4b(x - c) we get,
⇒ 4b = 2
⇒
⇒
We know that the distance between the vertex and focus is b.
∴The distance between the vertex and focus is .