Question

What is the equation of the parabola with a focus at (0, -5) and directrix y = 5?

	A.
	B.
	C.
	D.

 

Answer 1

The focus of the parabola is (0, -5) and directrix y = 5.

Since the directrix is y =5, the standard form of parabola equation is (x - h)^2 = 4p (y - k).

Find the value of h, k and p as follows :

The equation of directrix  y = k - p = 5 ⇒ k - p =     5 ------> (1).

Focus = (h, k + p) = (0, -5) ⇒ h = 0 and k + p = -5       ------> (2).

Solve equation 1 and 2, to obtain k = 0 and p = -5.

The standard form of parabola equation is (x - 0)^2 = 4(-5) (y - 0)

⇒ x² =-20y.

⇒ y=-(1/20) x²

So Option A ia correct.