SOLUTION: ihave to write this problem in its standard equation? 36x^2-288x+25y^2-150y=99

Question 170137: ihave to write this problem in its standard equation?
36x^2-288x+25y^2-150y=99
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation

Factor out 36 from the first two terms.

Factor out 25 from the last two terms.

Take half of the "x" coefficient -8 to get . Now square -4 to get

Add AND subtract the previous result 16 inside the first parenthesis

Take half of the "y" coefficient -6 to get . Now square -3 to get

Add AND subtract the previous result 9 inside the first parenthesis

Group the first three terms in both parenthesis

Factor to get . Factor to get

Distribute

Multiply

Combine like terms.

Add 801 to both sides.

Combine like terms.

Divide both sides by 900. We want the right side to be equal to 1.

Break up the fraction.

Reduce

Rewrite as . Rewrite as

So now the equation is in standard form (which is an ellipse), where , , , and

This means that the center of the ellipse is (4,3), the length of the minor axis is 2*5=10 units and the length of the major axis is 2*6=12 units

Note: the minor axis is horizontal and the major axis is vertical which means that the ellipse is slightly taller than it is wide.
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