Question

The equation of the red ellipse in the figure shown

Answer 1

Larger circle:

`x^2+y^2=81`

Smaller circle:

`x^2+y^2=49`

Explanation:

We have that the ellipse has the following equation:

`(x^(2))/(81)+(y^(2))/(49)=1`

Where 81 is the length of the major axis and 49 is the length of the minor axis.

These values also represent the radius squared of the circles.

For the larger circle the major axis would be 81, therefore the radius squared would also be 81.

The equation of a circle has the following form:

`x^2+y^2=r^2`

Therefore, the larger circle equation would be:

`x^2+y^2=81`

For the smaller circle the minor axis would be 49, therefore the radius squared would also be 49.

Therefore, the smaller circle equation would be:

`x^2+y^2=49`