Answer:
C
Step-by-step explanation:
You want the equations of the circle and ellipse in the given figure.
Equations
The standard form equation for an ellipse is ...
[tex]\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1[/tex]
where 'a' and 'b' are the semi-axes in the x-direction and y-direction, respectively.
You will notice that when a=b=r, the ellipse becomes a circle and the equation can be rewritten as ...
[tex]\dfrac{x^2}{r^2}+\dfrac{y^2}{r^2}=1\ \Longleftrightarrow\ x^2+y^2=r^2[/tex]
Application
Here, the radius is 3, the same as the semi-major axis in the x-direction (a=3). The ellipse axis in the y-direction appears to be about 1/3 that value, so b=1, and the equations of the circle and ellipse are ...
[tex]x^2+y^2=9\qquad\text{circle}\\\\\dfrac{x^2}{9}+\dfrac{y^2}{1}=1\qquad\text{ellipse}[/tex]
