Question

Ellipse standard equation & graphWrite the equation of the ellipse graphed below.

Answer 1

To answer this question we will use the following diagram as a reference:

Recall that the equation of a vertical ellipse is as follows:

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

where (h,k) is the ellipse's center, b is the semi-minor axis, and a is the semi-major axis.

From the given diagram we get that the ellipse's center is (4,4) its minor axis is 3, and the major axis is 4, therefore its equation is as follows:

$\frac{(x-4)^2}{3^2}+\frac{(y-4)^2}{4^2}=1.$

Answer:

$\frac{(x-4)^2}{9}+\frac{(y-4)^2}{16}=1.$