SOLUTION: If (4,5) and (6,1) are the endpoints of the diameter, write the equation of this circle. i dont know what formulas to use or how to actually solve this problem

Question 192952: If (4,5) and (6,1) are the endpoints of the diameter, write the equation of this circle. i dont know what formulas to use or how to actually solve this problem
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Step 1: Find the center of the circle

To find the center of the circle, you need to find the midpoint of the diameter with (4,5) and (6,1) as the endpoints. So simply average the corresponding coordinates to get:

. So the x-coordinate of the center is

. So the y-coordinate of the center is

So the center is (5,3). Since the center of

is (h,k), this means that and

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Step 2: Finding the radius

To find the radius, we need to find length of the diameter. To find the diameter's length, we need to find the distance from (4,5) to (6,1). To do that, we can use the distance formula:

Note: The point

is (4,5) which means that and . Similarly, the point

is (6,1) which 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 .

Factor to get .

Break up the square root.

Take the square root of to get .

So the diameter is units long. Take half of this length to get the radius:

So which means that the radius is units long

Since , this means that or just

Start with the general formula for a circle

Plug in and and

So the equation of the circle with the points (4,5) and (6,1) as the endpoints of the diameter is