Question

Find the axis, vertex, focus, equation of directrix and the length of latus rectum of the parabola (y - 2)² = 4(x - 1)

Answer 1

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

⇒ y² = 4X where X = x - 1 and Y = y - 2

⇒ 4a = 4

⇒ a = 1

	Referred to (X, Y)	Referred to (x, y) x = X + 1, Y = y + 2
Axis	X-axis ⇒ Y = 0	y - 2 = 0 ⇒ y = 2
Vertex	(0, 0)	(1, 2)
Focus (0, 0)	(1, 0)	(2, 2)
Equation of directrix	X = - a ⇒ X = - 1	x - 1 = - 1 ⇒ x = 0
Length of latus rectum	4a = 4	4