SOLUTION: How do I go about converting this equation to the standard form in order to graph the conic section? 4x^2-16x+9y^2+18y=0 I know I am supposed to complete the square...Thanks a bunc

Question 66491: How do I go about converting this equation to the standard form in order to graph the conic section? 4x^2-16x+9y^2+18y=0 I know I am supposed to complete the square...Thanks a bunch.
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
Conic Sections Summary --

If the coefficients of and are of the same sign, but unequal coefficients, then the graph will be an ELLIPSE.

If both coefficients are the same sign with equal coefficients, it will be a CIRCLE.

If coefficients are of opposite sign, then it will be a HYPERBOLA.

A PARABOLA results when there is an but no or a but no .

The preferred method of solving such a problem is the method of completing the square:

You must first factor out the coefficients of x^2 and y^2 like this:

This is an ellipse. The standard form for an ellipse is in a form = 1, so divide both sides of the equation by 25 to set it equal to 1.

Finally invert the coefficients of 4 and 9 in order to write this:

That would be standard form for an ellipse! The center is at (2,-1), with the "radius" extending units in the x direction, and units in the y direction.

R^2 at SCC

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