Question

If the foci of an ellipse are $(-4,4)and(6,4)$, then the coordinates of the center of the ellipse are _____ .

Short answer

If the foci of an ellipse are $(-4,4)and(6,4)$, then the coordinates of the center of the ellipse are role="math" localid="1646847484430" $\mathbf{(}\mathbf{1}\mathbf{,}\mathbf{4}\mathbf{)}$ .

Step-by-step solution

Step 1. Given Information

We want to fill the gap in the given equation with the missing terms.

We know that

Property of ellipse: In any ellipse, its center is the mid-point between the two foci and located on the major axis.

Step 2. Method to solve:

We are going to sue the following formula to determine the midpoint of the two given points.

If the given points are $(x_1,y_1)and(x_2,y_2)$then their midpoint is:$\left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)$

Step 4. Finding the center:

Plug in $(x_1,y_1)=(-4,4)and(x_2,y_2)=(6,4)$in the previous formula

$\left(\frac{-4+6}{2},\frac{4+4}{2}\right)=\left(\frac{2}{2},\frac{8}{2}\right)=\left(1,4\right)$