Question

Write the equation for the larger circle shown in the figure.

Answer 1

Answer:

See below for answers

Step-by-step explanation:

Given equation of the horizontal ellipse: $\frac{x^{2}}{64}+\frac{y^{2}}{16}=1$

Standard form: $\frac{x^{2}}{a^{2} }+\frac{y^{2}}{b^{2} }=1$

Values of a and b: $\frac{x^{2}}{8^{2} }+\frac{y^{2}}{4^{2} }=1$

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 $(x-h)^2+(y-k)^2=r^2$, then:

The equation for the larger circle is $x^{2} +y^{2} =8^{2}$

The equation for the smaller circle is $x^{2} +y^{2} =4^{2}$