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 4(y - 1) 2 = - 7(x - 3)

Philoid · Accepted Answer

Given equation of the parabola is 4(y - 1)² = - 7(x - 3)

⇒

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

⇒

⇒ The vertex is (c, a) = (3, 1)

⇒ The focus is (- b + c, a) =

⇒ The equation of the axis is y - a = 0 i.e, y - 1 = 0

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

⇒ Directrix is

⇒ Length of latus rectum is 4b .