Question

Find the focus of the parabola that has a vertex at (0, 0) and that passes through the points (4, 5) and (4, –5).

A. p=(-25/16,0)
B. p=(25/16,0)
C. p=(0,-25/16)
D. p=(100,0)

Answer 1

B. p=(25/16,0)

Explanation:

(y - k)2 = 4p (x - h) is the equation of a parabola since the axis of symmetry is is along x=0

Where (h,k) is the center

and (h+p, k) is the focus

The vertex is 0,0 so h and k are 0

(y - k)2 = 4p (x - h)

y^2 =4p (x)

We can use one of the points to determine p

5^2 =4*p*4

25 = 16p

Divide by 16

25/16 =p

focus = (25/16,0)