Find the vertex, focus, axis, directrix and lotus - rectum of the following parabolas
y² = 8x

Question

Find the vertex, focus, axis, directrix and lotus - rectum of the following parabolas y 2 = 8x

Philoid · Accepted Answer

Given parabola is y² = 8x. Comparing this with standard parabola y² = 4ax we get,

⇒ 4a = 8

⇒ a = 2

⇒ The vertex is (0, 0)

⇒ The focus is (a, 0) = (2, 0)

⇒ The equation of the axis is y = 0.

⇒ The equation of the directrix is x = - a i.e, x = - 2

⇒ The length of the latus rectum is 4a = 8.

Find the vertex, focus, axis, directrix and lotus - rectum of the following parabolasy2 = 8x