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 4x 2 = y

Philoid · Accepted Answer

Given parabola is 4x² = y.

Converting to standard form we get,

⇒

Comparing with standard parabola x² = 4ay we get,

⇒

⇒ The vertex is (0, 0)

⇒ The focus is (0, a) =

⇒ The equation of the axis is x = 0

⇒ The equation of the directrix is y = - a i.e, .

⇒ The length of the latus rectum is 4a = .