Question

Find the equation of the parabola with a vertex of (5, -2) and a focus of (5, -3)

Answer 1

Use the form
`\left(x-h\right)^2=(1)/(4p)\left(y-k \right)`
Then we have the vertex is
`(h,k)` and the distance from the vertex to the focus is p. Therefore we have
`\left(x-5\right)^2=-(1)/(4)\left(y+2\right)`. It is negative because the parabola is pointing downwards.

Answer 2

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