SOLUTION: How do I write the standard form equation for the circle with center (5,-4) and a point on the circle (1,1)?

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Question 1036820: How do I write the standard form equation for the circle with center (5,-4) and a point on the circle (1,1)?


Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
Center (h,k), radius r, standard form cirlce equation %28x-h%29%5E2%2B%28y-k%29%5E2=r%5E2. The radius is how far is any point on the circle to the center. The DISTANCE FORMULA gives the radius, r.

r=sqrt%28%285-1%29%5E2%2B%28-4-1%29%5E2%29----------simplify this.

Answer by ikleyn(52798) About Me  (Show Source):
You can put this solution on YOUR website!
.
How do I write the standard form equation for the circle with center (5,-4) and a point on the circle (1,1)?
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It is 

%28x-5%29%5E2+%2B+%28y-%28-4%29%29%5E2 = r%5E2,     or

%28x-5%29%5E2+%2B+%28y%2B4%29%5E2 = r%5E2,

where r is the radius of the circle.

To find the radius, calculate the distance from the center to the point.

It is sqrt%28%281-5%29%5E2+%2B+%281+-+%28-4%29%29%5E2%29 = sqrt%28%28-4%29%5E2+%2B+5%5E2%29 = sqrt%2816+%2B+25%29 = sqrt%2841%29.

So, yours equation is 

%28x-5%29%5E2+%2B+%28y%2B4%29%5E2 = 41.