Question

which ellipse is represented by the equation $\frac{(x - 3)^{2}}{25}+\frac{(y - 6)^{2}}{16}=1$?

Explanation:

Step1: Identify ellipse - center formula

The standard form of an ellipse is $\frac{(x - h)^2}{a^2}+\frac{(y - k)^2}{b^2}=1$, with center $(h,k)$.

Step2: Determine center

For $\frac{(x - 3)^2}{25}+\frac{(y - 6)^2}{16}=1$, $h = 3,k = 6$. So center is $(3,6)$.

Answer:

The ellipse has center $(3,6)$, semi - major axis $a = 5$ and semi - minor axis $b = 4$.