SOLUTION: Find the standard equation of a circle which is centered at (-4,3) and tangent to the line y=-4x-30

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Question 1042648: Find the standard equation of a circle which is centered at (-4,3) and tangent to the line y=-4x-30
Found 3 solutions by robertb, Alan3354, ikleyn:
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Rewrite the equation of the line as 4x + y +30 = 0.
===> The distance of the center (-4,3) of the circle from the tangential line
4x + y +30 = 0 is given by d+=+abs%284%2A-4%2B3%2B30%29%2Fsqrt%284%5E2%2B1%5E2%29+=+17%2Fsqrt%2817%29+=+sqrt%2817%29, which, incidentally, is also the radius of the circle.
===> the standard equation of circle is %28x%2B4%29%5E2%2B%28x-3%29%5E2+=+%28sqrt%2817%29%29%5E2, or
%28x%2B4%29%5E2%2B%28x-3%29%5E2+=+17.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Find the standard equation of a circle which is centered at (-4,3) and tangent to the line y=-4x-30
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Find the distance from the point to the line.
That's the radius.
Then %28x%2B4%29%5E2+%2B+%28y-3%29%5E2+=+r%5E2
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Answer by ikleyn(52751) About Me  (Show Source):
You can put this solution on YOUR website!
.
For the formula on the distance from a point to a straight line in a coordinate plane see the lesson
    - The distance from a point to a straight line in a coordinate plane
in this site.