Answer:
x^2 + y^2 -2x +y -71 = 0
Step-by-step explanation:
The center of the circle is the midpoint of the diameter, so is ...
((-3, -8) +(5, 7))/2 = (-3+5, -8+7)/2 = (1, -1/2)
The square of the radius of the circle can be found from the Pythagorean theorem. The x- and y- differences between an end point and the center are the legs of a right triangle with r as the hypotenuse.
r^2 = (5 -1)^2 +(7 -(-1/2))^2 = 4^2 +7.5^2 = 16 +56.25
r^2 = 72.25
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The standard form equation of the circle with center (h, k) and radius r is ...
(x -h)^2 +(y -k)^2 = r^2
(x -1)^2 +(y -(-1/2))^2 = 72.25
Eliminating parentheses, we have ...
x^2 -2x +1 +y^2 +y +0.25 = 72.25
Subtracting the right-side constant and rearranging to descending powers, we find the general form of the equation to be ...
x^2 + y^2 -2x +y -71 = 0
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Comment on the work
Of course, you know that ...
(a -b)^2 = a^2 -2ab +b^2
This helps you simplify the squares of binomials.
