a parabola has directrix x=6, axis y=5 and latus rectum equal to 9. Find its equation

Question

find its quation

Answer 1

Julie, we can tell this parabola is going to be sideways, given that our vertex is horizontal. Since the directrix is to the left of our focus (which the latus rectum runs through), we know that it's opening to the right and p is going to be positive.

 

(y - k)² = 4p(x - h)

 

Our vertex is halfway between the focus and the directrix, p must equal 1.5 and h must equal 7.5. 

 

h is equal to the axis, so our vertex is (7.5, 5)

 

(y - 5)² = 4(1.5)(x - 7.5)

(y - 5)² = 6(x - 7.5)

 

Hope this helps!