Find the equation of a parabola with focus (2, -3) and directrix x = 5.

Answer 1

It's a leftward opening horizontal parabola

focus (2,-3), directrix x = 5

vertex is half way between them (7/2,-3)

x = a(y+3)^2 +7/2, to find "a" the leading coefficient, plug in any other parabola point such as (2,0) which is 3 units from the focus, directly above, and 3 units from the directrix, directly to the left

0 = a(9)+7/2

a= -7/2/9=-7/18

x=-(7/18)(y+3)^2 + 7/2