Question

What is the equation of the parabola with a focus at (-3,1) and a directrix of y= -1?

Answer 1

`y=x^2/4+(3x)/2+9/4`

Explanation:

Given -
Focus `(-3, 1)`
Directrix `(y=-1)`

From the given information, we understand the parabola is opening up.

The vertex lies in between Focus and directrix at the middle.

The vertex is `(-3, 0)`

Then the vertex form of the equation is

`(x-h)^2=4xxaxx(y-k)`

Where -

`h= -3`
`k=0`
`a=1` The distance between focus and vertex or directrix and vertex.
`(x-(-3))^2=4 xx 1 xx( y-0)`
`(x+3)^2=4y`
`4y= x^2+6x+9`

`y=x^2/4+(3x)/2+9/4`