Find the standard form of the equation of the parabola with the given characteristics. Focus: (5, 5); directrix: x = −5

Answer 1

this is a rightward opening parabola since the directrix is to the left of the focus

the vertex is midway between the focus and directrix. Vertex = (0,5)

the standard form of the parabola is

x= a(y-k)^2 + h where vertex is (h,k) = (0,5)

x =a(y-5)^2 To find a plug in another point on the parabola, a point directly above the focus. (5,15) It's the same distance to the directrix as to the focus or 10. so the y coordinate = 5+10 = 15

5 =a(10)^2

a =5/100 = 1/20

x =(1/20)(y-5)^2 or

20x = y^2 -10y +25,