Question

What are the vertex, focus, and directrix of the parabola described by `(x − 5)^2 = −4(y + 2)`?

Answer 1

`(5,-2),(5,-3),y=-1`

Explanation:

`"the standard form of a vertically opening parabola is"`

`•color(white)(x)(x-h)^2=4a(y-k)`

`"where "(h,k)" are the coordinates of the vertex and a"`
`"is the distance from the vertex to the focus and"`
`"directrix"`

`(x-5)^2=-4(y+2)" is in this form"`

`"with vertex "=(5,-2)`

`" and "4a=-4rArra=-1`

`"Focus "=(h,a+k)=(5,-1-2)=(5,-3)`

`"directrix is "y=-a+k=1-2=-1`
graph{(x-5)^2=-4(y+2) [-10, 10, -5, 5]}