Find the vertex, focus, axis, directrix and lotus - rectum of the following parabolas
x2 + y = 6x – 14
Given equation of the parabola is x2 + y = 6x - 14
⇒ x2 - 6x = - y - 14
⇒ x2 - 6y + 9 = - y - 5
⇒ (x - 3)2 = - (y + 5)
Comparing with the standard form of parabola (x - a)2 = - 4b(y - c) we get,
⇒ 4b = 1
⇒
⇒ The vertex is (a, c) = (3, - 5)
⇒ The focus is (a, - b + c) =
⇒ The equation of the axis is x - a = 0 i.e, x - 3 = 0
⇒ The equation of the directrix is y - c = b
⇒ Directrix is
⇒ The directrix is
⇒ Directrix is
⇒ Length of latus rectum is 4b = 1.