Question

Write the standard form of the equation of the parabola with the given focus or directrix and

vertex (0, 0).
focus: (5, 0)

Answer 1

x = 1/20 y^2

Explanation:

This is a rightward opening (sideways ) parabola

Directrix = x = -5

Distance formula form point x,y to directrix and focus are equal:

(x - -5)^2 = (x-5)^2 + y^2

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

20x = y^2

x = 1/20 y^2