SOLUTION: Hello, I have a question regarding formulas and equations. So, i tried to figure out this problem, however, I am not sure if the answer is correct: is the graph of 11x - x^2

SOLUTION: Hello, I have a question regarding formulas and equations. So, i tried to figure out this problem, however, I am not sure if the answer is correct: is the graph of 11x - x^2 - 4

Question 288363: Hello, I have a question regarding formulas and equations.
So, i tried to figure out this problem, however, I am not sure if the answer is correct:
is the graph of 11x - x^2 - 4y^2 = 2y - 16 the graph of an ellipse?
I am not sure...thank you for your time:)
Found 2 solutions by jim_thompson5910, Alan3354:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Subtract 2y from both sides and rearrange the terms.

Complete the square for the x terms. Let me know if you need me to show you how to complete the square.

Complete the square for the y terms

Combine like terms

Subtract from both sides

Combine like terms

Reduce.

Multiply every term (outside the parenthesis) by -1.

Multiply every term (outside the parenthesis) by to make the right side equal to 1.

Rewrite as . Rewrite as .

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

So is an ellipse.

Consequently, is also an ellipse (since the two equations are equivalent).

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
There's an x^2 term and a y^2 term, and their signs are the same.
--> ellipse

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