Question

What type of conic section has the equation `4x^2 - y^2 +4y - 20= 0`?

Answer 1

`4x^2-y^2+4y-20=0`

`4x^2-y^2+4y=20`

`4(x-0)^2-y^2+4y=20`

We need to complete the square using the `y` term.

`(4/2)^2=(2)^2=4`, Add `4` to both sides

`4(x-0)^2-y^2+4y+4=20+4`

`y^2+4y+4 =>(y+2)^2=>` Perfect square trinomial

Re-write:

`4(x-0)^2-(y+2)^2=20+4`

`4(x-0)^2-(y+2)^2=24`

`(4(x-0)^2)/24-((y+2)^2)/24=24/24`

`((x-0)^2)/6-((y+2)^2)/24=1=>`Hyperbola