SOLUTION: The endpoints of a diameter of a circle are (-2,1) and (6, -5). Write the standard equationof the circle?

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Question 40114This question is from textbook geometry, measuring, reasoning, applying
: The endpoints of a diameter of a circle are (-2,1) and (6, -5).
Write the standard equationof the circle? This question is from textbook geometry, measuring, reasoning, applying

Found 2 solutions by longjonsilver, Nate:
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
1. find the origin of the circle by finding the midpoint between the 2 quoted points.

2. Calculate the length of the diameter using the standard formula for length of a line. Find the radius from this length by dividing by 2.

3. Find the standard equation of a circle and put in the values of the coordinates of the centre and the length of the radius.

Done.


Jon.

Answer by Nate(3500) About Me  (Show Source):
You can put this solution on YOUR website!
The midpoint of the diameter is the centre.
Midpoint formula: (%28x+%2B+x%29%2F2,%28y+%2B+y%29%2F2)
(%28-2+%2B+6%29%2F2,%281+-+5%29%2F2)
(%284%29%2F2,%28-4%29%2F2)
(2,-2)
The distance from this point to a another point on the circle is the radius.
Distance formula: d+=+sqrt%28%28x+-+x%29%5E2+%2B+%28y+-+y%29%5E2%29
d+=+sqrt%28%282+%2B+2%29%5E2+%2B+%28-2+-+1%29%5E2%29
d+=+sqrt%28%284%29%5E2+%2B+%28-3%29%5E2%29
d+=+sqrt%2816+%2B+9%29
d+=+sqrt%2825%29
d+=+5
Standard form for circle: %28x+-+h%29%5E2+%2B+%28y+-+k%29%5E2+=+r%5E2
%28x+-+2%29%5E2+%2B+%28y+%2B+2%29%5E2+=+25