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musiclover10045

The equation of a circle is written as (x-h)^2 + (y-k)^2 = r^r

H and k are the x and y coordinates of the center of the circle and r is the radius.

You are given the diameter coordinates so find the halfway point for the center then calculate the radius

Midpoint = (x1 +x2)/2, (y1 + y2)/2

Midpoint = (7 + -1)/2, (-3 +7)/2

Midpoint = 6/2, 4/2

Midpoint = 3,2

So h = 3 and k = 2

Now find radius by finding the distance between the center point and an end point.

Distance = sqrt(41)

Equation of the circle:

(X-3)^2 + (y-2)^2 = 41

manissaha129

Answer:

The equation of the circle is written as:

(x-h)²+(y-k)²=r²

'h' and 'k' are the x and y coordinates of the center of the circle and 'r' is the radius.

You are given that the diameter coordinates, so find the halfway point for the center then calculate the radius

[tex]Midpoint = ( \frac{x_1 + x_2 }{2}, \frac{y_1 + y_2}{2} ) \\ = ( \frac{7 + ( - 1)}{2} , \frac{ (- 3 )+ 7}{2} ) \\ = ( \frac{6}{2} ,\frac{4}{2} ) = (3,2)[/tex]

So, h=3 and k=2

Now find the radius by finding the distance between the center point and the end point.

Distance=√{(7-3)²+(-3-2)²}=√{(4)²+(-5)²} =√{16+25}=√41

Equation of the circle:

(x-3)²+(y-2)²=41 ✓

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