Answer:
See below for answers
Step-by-step explanation:
Given equation of the horizontal ellipse: [tex]\frac{x^{2}}{64}+\frac{y^{2}}{16}=1[/tex]
Standard form: [tex]\frac{x^{2}}{a^{2} }+\frac{y^{2}}{b^{2} }=1[/tex]
Values of a and b: [tex]\frac{x^{2}}{8^{2} }+\frac{y^{2}}{4^{2} }=1[/tex]
Therefore, the radius of the bigger circle is a=r=8 (half the length of the major axis) and the radius of the smaller circle is b=r=4 (half the length of the minor axis).
Given the equation for a circle is [tex](x-h)^2+(y-k)^2=r^2[/tex], then:
The equation for the larger circle is [tex]x^{2} +y^{2} =8^{2}[/tex]
The equation for the smaller circle is [tex]x^{2} +y^{2} =4^{2}[/tex]
