Write a circle equation

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Malakuka7

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This is the problem: write the circumference /circle equation, which touches A(2,0) and also touches a circumference, which is given by (x+2)^2 +(y-8)^2 =100, from the inside. So far all i've figured out is that p=2 , q=r and that the circumference we need to find is inside the given one.
 
Malakuka7 said:
This is the problem: write the circumference /circle equation, which touches A(2,0) and also touches a circumference, which is given by (x+2)^2 +(y-8)^2 =100, from the inside. So far all i've figured out is that p=2 , q=r and that the circumference we need to find is inside the given one.
Click to expand...
Please share your work.

You said: i've figured out is that p=2 , q=r

What is 'p'? What is 'r'?

Please share your work.
 
Malakuka7 said:
This is the problem: write the circumference /circle equation, which touches A(2,0) and also touches a circumference, which is given by (x+2)^2 +(y-8)^2 =100, from the inside. So far all i've figured out is that p=2 , q=r and that the circumference we need to find is inside the given one.
Click to expand...
I don't think there is sufficient information. There are infinitely many circles that pass through (2,0) and a internally tangent to the circle with center (-2,8) and radius 10. I can see this by merely sketching the situation and thinking about where this circle might be.

Have you stated the entire problem, exactly as given to you?
 
Malakuka7 said:
This is the problem: write the circumference /circle equation, which touches A(2,0) and also touches a circumference, which is given by (x+2)^2 +(y-8)^2 =100, from the inside. So far all i've figured out is that p=2 , q=r and that the circumference we need to find is inside the given one.
Click to expand...
You said:

i've figured out is that p=2 , q=r

How? Please show work.
 
Malakuka7 said:
P is the x coordinate of the center of circle i need to find, q is the y coordinate and r is radius.
Click to expand...
This, with your statement that p=2 , q=r, suggests that what you omitted is that the circle touches the x-axis at (2,0). Is that correct? In that case, your work is (almost) correct as far as you got, but that is not very far.

You might just write the equation of the circle with center (2, -r) and radius r, and try to solve that equation together with the given equation. You want there to be exactly one solution. Am I right in supposing that you are to solve this algebraically rather than geometrically?
 
Dr.Peterson said:
This, with your statement that p=2 , q=r, suggests that what you omitted is that the circle touches the x-axis at (2,0). Is that correct? In that case, your work is (almost) correct as far as you got, but that is not very far.

You might just write the equation of the circle with center (2, -r) and radius r, and try to solve that equation together with the given equation. You want there to be exactly one solution. Am I right in supposing that you are to solve this algebraically rather than geometrically?
Click to expand...
Yes it is correct, that the circle touches the x axis at A(2,0). As far as i can tell there are 2 solutions, one circle is above the x axis and one is below. And yes, i do have to solve this algebraically.
I know i must somehow connect the known circle equation with the one im searching for, but i dont know how.
 
Please make an attempt, so we have something specific to talk about. At least write the two equations, and do something to try to eliminate a variable (even if it doesn't do what you want). Then show us what you've done.

Also, it may help if you tell us what topics you have been studying that might be relevant. Have you learned any specific ways to solve a system of nonlinear equations, for example?
 
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