Find the vertex, focus, axis, directrix and lotus - rectum of the following parabolas

Question

Find the vertex, focus, axis, directrix and lotus - rectum of the following parabolas y 2 + 4x + 4y - 3 = 0

Philoid · Accepted Answer

Given equation of the parabola is y² + 4x + 4y - 3 = 0

⇒ y² + 4y = - 4x + 3

⇒ y² + 4y + 4 = - 4x + 7

⇒

Comparing with the standard form of parabola (y - a)² = - 4b(x - c) we get,

⇒ 4b = 4

⇒ b = 1

⇒ The vertex is (c, a) =

⇒ The focus is (- b + c, a) =

⇒ The equation of the axis is y - a = 0 i.e, y + 2 = 0

⇒ The equation of the directrix is x - c = b

⇒ Directrix is

⇒ Length of latus rectum is 4b = 4.