SOLUTION: a circle touches the circle (x+1)^2+y^2=9 and passes through (1,0). find the locus of its center. PLEASE GIVE SOLUTION (ANSWER: 20x^2+36y^2=45).thx XD

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: a circle touches the circle (x+1)^2+y^2=9 and passes through (1,0). find the locus of its center. PLEASE GIVE SOLUTION (ANSWER: 20x^2+36y^2=45).thx XD      Log On


   

Question 912053: a circle touches the circle (x+1)^2+y^2=9 and passes through (1,0). find the locus of its center. PLEASE GIVE SOLUTION (ANSWER: 20x^2+36y^2=45).thx XD
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a circle touches the circle (x+1)^2+y^2=9 and passes through (1,0). find the locus of its center. PLEASE GIVE SOLUTION (ANSWER: 20x^2+36y^2=45).thx XD
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Do you mean it's tangent to the circle?
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(1,0) is inside the given circle, so the circles will be internally tangent.
The radius of (x+1)^2+y^2=9 is 3.
The center of the circles is (h,k)
The distance from (h,k) to (1,0) = sqrt%28k%5E2+%2B+%28h-1%29%5E2%29
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The distance also equals 3 - [the distance from (h,k) to (-1,0)]
= 3+-+sqrt%28%28h%2B1%29%5E2+%2B+k%5E2%29
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sqrt%28%28h%2B1%29%5E2+%2B+k%5E2%29+=+3+-+sqrt%28k%5E2+%2B+%28h-1%29%5E2%29


4h+-+9+=+-6sqrt%28k%5E2+%2B+%28h-1%29%5E2%29
16h%5E2+-+72h+%2B+81+=+36%2A%28k%5E2+%2B+h%5E2+-+2h+%2B+1%29
16h%5E2+-+72h+%2B+81+=+36k%5E2+%2B+36h%5E2+-+72h+%2B+36%29
16h%5E2+%2B+45+=+36k%5E2+%2B+36h%5E2%29
+45+=+36k%5E2+%2B+20h%5E2%29
36k%5E2+%2B+20h%5E2+-+45+=+0%29
Sub x & y for (h,k)
20x%5E2+%2B+36y%5E2+=+45