Write an equation with the given focus and directrix.
a. focus: (5,2); directrix: x-axis
b. focus: (-2,3); directrix: the line y=7
c. focus: (0,7); directrix: x-axis
d. focus: (-3, -4); directrix: the line y=-1
a. For a focus at (5,2) and directrix at the x-axis, the equation is:
((x-5)^2 + (y-2)^2 = (y+2)^2)
b. For a focus at (-2,3) and a directrix at y=7, the equation is:
((x+2)^2 + (y-3)^2 = 16(y-7))
c. For a focus at (0,7) and a directrix at the x-axis, the equation is:
((x-0)^2 + (y-7)^2 = (y+7)^2)
d. For a focus at (-3,-4) and a directrix at y=-1, the equation is:
((x+3)^2 + (y+4)^2 = 25(y+1))