SOLUTION: Can you show a step by step process of how to put 25x^2+16y^2+150x=160y-225 into standard form for an ellipse?

Question 442903: Can you show a step by step process of how to put 25x^2+16y^2+150x=160y-225 into standard form for an ellipse?
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!

Start with the given equation.

Subtract 160y from both sides.

Group like terms.

Factor 25 from the first group (to make the coefficient equal to 1)

Factor 16 from the second group (to make the coefficient equal to 1)

Take half of the "x" coefficient 6 to get 3. Square 3 to get 9. Add AND subtract this value inside the first parenthesis:

Add AND subtract 9 in the first parenthesis.

Factor to get

Take half of the "y" coefficient -10 to get -5. Square -5 to get 25. Add AND subtract this value inside the second parenthesis:

Add AND subtract 25 in the second parenthesis.

Factor to get

Distribute

Multiply

Combine like terms.

Add 625 to both sides.

Combine like terms.

Divide both sides by 400 (to make the right side equal to 1)

Break up the fraction.

Reduce

Rewrite 16 as . Rewrite 25 as

Rewrite as

Now the equation is in the form which is the standard form of an ellipse where , , and

So the value of is
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