Can someone please be kind and show me the steps on this? Thanks

Question

Find the equation of the circle centered at the origin in the uv-plane that has twice the circumference of the circle whose equation equals
(u-5)^2 + y^2 =9

Answer 1

The general equation of a circle is
(x-x0)² + (y-y0)² = r²
where (x0,y0) represent the centre of the circle, and r = radius.

The given equation of the circle:
(u-5)^2 + y^2 =9
can be rewritten as:
(u-5)² + (y-0)² = 3²
which tells us that the circle has a centre at (5,0) with a radius of 3.

The circumference is therefore 2π(3)=6π

The new circle is to have twice the circumference, 12π so the radius must be 6.
The centre is at the origin, i.e. (0,0).
So the equation of the required circle is therefore:
(u-0)²+(v-0)²=6²
Simplifying,
u²+v²=36

Answer 2

Thank you very, very much Mathmate for your help I appreciate the time you took to show me the step by step...Again many thanks