SOLUTION: Please help sketch the graph and name the conic section with equation: 4x^2-16x+9y^2+18y=0 So far I have factored out the 4 and 9. What comes next?Thank you

Question 66246: Please help sketch the graph and name the conic section with equation:
4x^2-16x+9y^2+18y=0 So far I have factored out the 4 and 9. What comes next?Thank you
Found 2 solutions by checkley71, rapaljer:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
4X^2-16X+9Y^2+18Y=0
4X(X-4)+9Y(Y+2)=0
(graph 300x200 pixels, x from -6 to 5, y from -20 to 20,4x^2 -16x +9y^2 +18y).
Answer by rapaljer(4671) (Show Source): You can put this solution on YOUR website!
I'm afraid the other solution that was posted for this problem is incorrect. Anytime you have an equation of a conic section with and with both having positive but unequal coefficients, it will be an ELLIPSE, NOT a PARABOLA.

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 .

This is the way it should be solved by 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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