SOLUTION: Write the equation of the circle that has a diameter whose endpoints are located at (-2,-1) and (4,-1).

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Question 189960This question is from textbook saxon algebra 2
: Write the equation of the circle that has a diameter whose endpoints are located at (-2,-1) and (4,-1). This question is from textbook saxon algebra 2

Answer by jojo14344(1513) About Me  (Show Source):
You can put this solution on YOUR website!


We know the Standard Eqn of a circle ---> %28x-h%29%5E2+%2B+%28y-k%29%5E2+=+r%5E2

Let us see the circle with endpoints A(-2,-1) & B(4,-1). In doing so, we get the midpoint at x & y:

X: %28x%5B1%5D%2Bx%5B2%5D%29%2F2=%28-2%2B4%29%2F2=2%2F2=red%281%29
Y: %28y%5B1%5D%2By%5B2%5D%29%2F2=%28-1%2B%28-1%29%29%2F2=-2%2F2=red%28-1%29
Midpoint: (1,-1)--> (h,k)



For the radius = (1/2)*Diameter

And the Diameter equals the Distance of the endpoints A and B.

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

D=sqrt%2836%29=6

And, radius=%281%2F2%29D=%281%2F2%29%286%29=red%283%29

Therefore, it follows---> %28x-1%29%5E2+%2B+%28y-%28-1%29%29%5E2+=3%5E2} ---> red%28%28x-1%29%5E2%2B%28y%2B1%29%5E2=9%29, Answer


Thank you,
Jojo