SOLUTION: Write an equation for each circle. A circle with center at (-2,-7) and a radius with endpoints (0,7)

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Question 742483: Write an equation for each circle. A circle with center at (-2,-7) and a radius with endpoints (0,7)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Equation: %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2

given: center (h,k)=(-2,-7), radius with endpoints (0,7); so, r will be the distance between (-2,-7) and (0,7)
Solved by pluggable solver: Distance Formula


The first point is (x1,y1). The second point is (x2,y2)


Since the first point is (-2, -7), we can say (x1, y1) = (-2, -7)
So x%5B1%5D+=+-2, y%5B1%5D+=+-7


Since the second point is (0, 7), we can also say (x2, y2) = (0, 7)
So x%5B2%5D+=+0, y%5B2%5D+=+7


Put this all together to get: x%5B1%5D+=+-2, y%5B1%5D+=+-7, x%5B2%5D+=+0, and y%5B2%5D+=+7

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Now use the distance formula to find the distance between the two points (-2, -7) and (0, 7)



d+=+sqrt%28%28x%5B1%5D-x%5B2%5D%29%5E2+%2B+%28y%5B1%5D+-+y%5B2%5D%29%5E2%29


d+=+sqrt%28%28-2+-+0%29%5E2+%2B+%28-7+-+7%29%5E2%29 Plug in x%5B1%5D+=+-2, y%5B1%5D+=+-7, x%5B2%5D+=+0, and y%5B2%5D+=+7


d+=+sqrt%28%28-2%29%5E2+%2B+%28-14%29%5E2%29


d+=+sqrt%284+%2B+196%29


d+=+sqrt%28200%29


d+=+sqrt%28100%2A2%29


d+=+sqrt%28100%29%2Asqrt%282%29


d+=+10%2Asqrt%282%29


d+=+14.142135623731

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Answer:


The distance between the two points (-2, -7) and (0, 7) is exactly 10%2Asqrt%282%29 units


The approximate distance between the two points is about 14.142135623731 units



So again,


Exact Distance: 10%2Asqrt%282%29 units


Approximate Distance: 14.142135623731 units




so, r=14.14, then
%28x%2B2%29%5E2%2B%28y%2B7%29%5E2=14.14%5E2
%28x%2B2%29%5E2%2B%28y%2B7%29%5E2=199.9396