Question

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

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

Answer 1

See below for answers

Explanation:

Given equation of the horizontal ellipse:
`(x^(2))/(64)+(y^(2))/(16)=1`

Standard form:
`(x^(2))/(a^(2) )+(y^(2))/(b^(2) )=1`

Values of a and b:
`(x^(2))/(8^(2) )+(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)`