Quiz 8.2, #3
The two terms, 16x^2+9y^2 imply that this conic section must be either an ellipse or a circle. We know that it will only be a circle if the horizontal scale factor, a, is equivalent to the vertical scale factor, b. That is, we will only have a circle if a=b. First rearrange all of the terms in the given problem. Then complete the square for the x's. (Remember, to Complete the Square, we first need the form x^2+bx) Next complete the square for the y's. (Remember to Complete the Square, we first need the form y^2+by) Based on the general form, we know that the right-hand-side of the equation must be equal to 1, so divide. Rearrange and simplify until we have the ELLIPSE (a is not equal to b) in General Form. From here, it is easy to tell that a=3, b=4, h=-5 and k=2... that is, the center of the Ellipse is located at the point C=(-5,2).