Question

How do I graph the ellipse with the equation `x^2+4y^2-4x+8y-60=0`?

Answer 1

An ellipse centered at `(2, –1)` with horizontal radius `sqrt(68)` units and vertical radius `sqrt(17)` units.

Explanation:

Firstly, complete the square.

`x^2 - 4x + 4y^2 + 8y = 60`
`x^2 - 2(2)x + 2^2 + 4(y^2 + 2(1)y + 1^2) = 60 + 2^2 + 4`
`(x-2)^2 + 4(y+1)^2 = 68`
`(x-2)^2/68 + (y+1)^2/17 = 1`
`(x-2)^2/(sqrt(68))^2 + (y+1)^2/(sqrt(17))^2 = 1`

Thus the graph is an ellipse centered at `(2, –1)` with horizontal radius `sqrt(68)` units and vertical radius `sqrt(17)` units.