SOLUTION: Given the endpoints of a diameter of a circle at (4,1) and (-4,-4), find the center and radius of the circle. Write its equation in standard form. Thanks in advance for your h

Question 779326: Given the endpoints of a diameter of a circle at (4,1) and (-4,-4), find the center and radius of the circle. Write its equation in standard form.
Thanks in advance for your help.
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
if the endpoints of a of a circle at (4,1) and (-4,-4), then the center is midpoint:
coordinate of midpoint is
coordinate of midpoint is
so, the center is at (,) and it means and
now find the length of radius which is equal to distance between one endpoint and midpoint of diameter

Solved by pluggable solver: Distance Formula

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

Since the first point is (0, -1.5), we can say (x1, y1) = (0, -1.5)
So ,

Since the second point is (4, 1), we can also say (x2, y2) = (4, 1)
So ,

Put this all together to get: , , , and

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Now use the distance formula to find the distance between the two points (0, -1.5) and (4, 1)

Plug in , , , and

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Answer:

The distance between the two points (0, -1.5) and (4, 1) is exactly units

The approximate distance between the two points is about 4.7169905660283 units

So again,

Exact Distance: units

Approximate Distance: units

so, radius is
equation of a circle in standard form:

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