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

1 Answer
Joel Kindiak · sente
Jun 6, 2016

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.

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