SOLUTION: Find an equation(s) of the circle(s) tangent to 2x - 3y + 6 = 0 at (3,4); center on 3x + 2y - 17 = 0

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Question 835835: Find an equation(s) of the circle(s) tangent to 2x - 3y + 6 = 0 at (3,4); center on 3x + 2y - 17 = 0
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find an equation(s) of the circle(s) tangent to 2x - 3y + 6 = 0 at (3,4); center on 3x + 2y - 17 = 0
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The 2 lines intersect at (3,4) --> an infinite # of circles that fit.
3x + 2y - 17 = 0
y = -3x/2 + 17/2
Pick any point on the line and find its distance from (3,4)
Use (h,k) for the point
d%5E2+=+%28k-4%29%5E2+%2B+%28h-3%29%5E2
d is the radius
%28x-h%29%5E2+%2B+%28y-k%29%5E2+=+d%5E2
x%5E2+-+2hx+%2B+h%5E2+%2B+y%5E2+-+2ky+%2B+k%5E2+=+%28k-4%29%5E2+%2B+%28h-3%29%5E2
x%5E2+-+2hx+%2B+h%5E2+%2B+y%5E2+-+2ky+%2B+k%5E2+=+k%5E2-8k%2B16+%2B+h%5E2-6h%2B9
x%5E2+-+2hx+%2B+y%5E2+-+2ky+=+-8k+-+6h+%2B+25
x%5E2+-+h%282x+-+6%29+%2B+y%5E2+-+k%282y+-+8%29+=+25
y = -3x/2 + 17/2 --> k = -3h/2 + 17/2
x%5E2+-+h%282x+%2B+6%29+%2B+y%5E2+%2B+%283h-17%29%28y+-+4%29+=+25
x%5E2+-+h%282x+%2B+6%29+%2B+y%5E2+%2B+3hy+-+12h+-+17y+%2B+68+=+25
x%5E2+-+h%282x+-+3y+%2B+6%29+%2B+y%5E2+-+17y+%2B+43+=+0
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Pick any value for h and you get a circle that fits.