Asked by Ann
Can someone please be kind and show me the steps on this? Thanks
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
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
Answers
Answered by
MathMate
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
(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
Answered by
Amy
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
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.