SOLUTION: I'm stuck on a question, please help!! :) " Determine the equation of a circle with a diameter whose endpoints are P(5,-6) and Q(1,2)" I used the midpoint formula and got (3

Question 397031: I'm stuck on a question, please help!! :)
" Determine the equation of a circle with a diameter whose endpoints are P(5,-6) and Q(1,2)"
I used the midpoint formula and got (3,-2) for the midpoint, and then sketched out the graph and ended up with 8 for the hypotenuse and 4 for the other side. So then I went
"PQ=4^2+8^2=16 =16+64=80 "
and then went
" PQ = sqrt ( 80 ) "
And now I'm stuck! How do I finish the question? And am I even doing this right??
Found 2 solutions by jim_thompson5910, robertb:
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
You find the midpoint, which is the center of the circle. Since you found the midpoint to be (3,-2), this means that the center of the circle is (3,-2). This is only possible because the line segment PQ is the diameter.

Recall that the equation of the circle with radius 'r' and center (h,k) is

So because the center of the circle is (3,-2), this means that and . Plug these values into the equation above to get

and simplify to get

So all we need to find out is the value of . So we need to find the value of the radius 'r'. It turns out that the distance from the center (3,-2) to either point will be equal to the radius (draw a picture if you're not sure)

So to find 'r', let's find the distance from P(5,-6) to the center (3,-2)

Note: is the first point . So this means that and .
Also, is the second point . So this means that and .

Start with the distance formula.

Plug in , , , and .

Subtract from to get .

Subtract from to get .

Square to get .

Square to get .

Add to to get .

So this distance is units. So

This then means that

So

Plug this last value into the equation from the beginning to get

So the equation of the circle with a diameter whose endpoints are P(5,-6) and Q(1,2) is

If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim
Answer by robertb(5830) (Show Source): You can put this solution on YOUR website!
You are right that PQ = . Remember that this is the LENGTH OF THE DIAMETER, and so to get the radius you only have to divide this by 2:
Radius =
The equation of the circle is then .
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