SOLUTION: A circle passes through (3,5) and(1,2) ,find its equation

Question 551091: A circle passes through (3,5) and(1,2) ,find its equation
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
I'm assuming that these are the endpoints of the diameter.

Recall that the general equation of a circle is .

So we need the center (h,k) and the radius squared .

First, let's find the center (h,k).

Since the center is the midpoint of the line segment with endpoints (3,5) and (1,2), we need to find the midpoint.

X-Coordinate of Midpoint =

Since the x coordinate of midpoint is , this means that

Y-Coordinate of Midpoint =

Since the y coordinate of midpoint is , this means that

So the center is the point (2, 7/2)

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Now let's find the radius squared

Use the formula , where (h,k) is the center and (x,y) is an arbitrary point on the circle.

In this case, and . Also, and . Plug these values into the equation above and simplify to get:

So because , , and , this means that the equation of the circle that passes through the points (3,5) and (1,2) (which are the endpoints of the diameter) is

.

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