Question

Find an equation of the parabola with vertex (5,4) and directrix y=9

Answer 1

Answer:
`(x-5)^2=-20(y-4)`

Explanation:

Given

Vertex of parabola is
`(5,4)`

and directrix is
`y=9`

as directrix is above vertex so it downward facing parabola

Distance between directrix and parabola is

`\mid 9-4\mid=5`

so value of
`a=5`

Equation of parabola is

`(x-5)^2=-4a(y-4)`

`(x-5)^2=-4(5)(y-4)`

`(x-5)^2=-20(y-4)`