Find an equation of the circle that satisfies the stated conditions. (Give your answer in standard notation.) Endpoints of a diameter A(−6, 3) and B(4, 7)

Equation of circle is:

Step-by-step explanation:

We need to find an equation of the circle that satisfies the stated conditions. (Give your answer in standard notation.)

Endpoints of a diameter A(−6, 3) and B(4, 7)

The general equation of circle is:

Where r is radius and (h,k) is centre of circle.

Finding centre of circle

The midpoint of diameter is centre of circle.

So, finding midpoint of A(−6, 3) and B(4, 7)

The formula used is:

We have x_1=-6, y_1=3, x_2=4, y_2=7

So, we get Midpoint (x,y)=(-1,5)

Finding radius of circle

Radius of circle can be found by first finding diameter using distance formula and then divide it by 2.

So, Diameter = 10.77

Radius = Diameter/2 = 5.38

Equation of circle

Equation of circle having centre(-1,5) and radius r = 5.38 is:

So, Equation of circle is:

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