SOLUTION: Classify the conic section. (State whether it is a hyperbola, ellipse, circle or parabola). Be sure to use correct spelling or your answer will be marked wrong. 16x^2 + 9y^2 + 24x

Question 288643: Classify the conic section. (State whether it is a hyperbola, ellipse, circle or parabola). Be sure to use correct spelling or your answer will be marked wrong. 16x^2 + 9y^2 + 24x - 36y + 23 = 0
Also my teacher said that this problem couldnt be an ellipse because I originally thought thats what this was but unfortunately its not so thats why I'm confused, please help!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation.

Subtract 23 from both sides

Group like terms.

Factor out the leading terms from each group (to make their coefficients equal to 1).

Complete the square for each group (let me know if you need help with that)

Group the first three terms in each group.

Factor each grouped trinomial.

Distribute.

Combine like terms.

Add 45 to both sides.

Combine like terms.

Divide every term outside the parenthesis by 22 to make the right side equal to 1.

Rearrange the terms.

So is an equation in the form of where , , and .

Recall that is the general equation of an ellipse. So is an ellipse.

Because is equivalent to , this means that is also an ellipse.

So is an ellipse.

So either there's a typo or your teacher is mistaken.
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