Question

Which conic section does the equation below describe?

Answer 1

Answer: Option C. Ellipse

Step-by-step explanation:

The general equation of an ellipse has the following form:

$\frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} =1$

Where the point (h, k) is the center of the ellipse

In this case we have the equation

$\frac{(x-9)^2}{4} + \frac{(y+2)^2}{25} =1$

Note that its shape matches that of a ellipse with center (9, -2)

$a=\sqrt{4} \\a=2\\\\\\b=\sqrt{25}\\b=5$

Therefore the answer is the obtion C