Question

A diameter of a circle has endpoints p(-10,-2) and Q(4,6)

a find the center of the circle.
b. Find the radius radical form
c.write an equation for the circle

Answer 1

a) center: (-3, 2)

b) radius: √65

c) equation: (x +3)² +(y -2)² = 65

Explanation:

a) The center (point A) is the midpoint of the diameter, so its coordinates are the average of the endpoint coordinates:

A = (P +Q)/2 = ((-10, -2) +(4, 6))/2

= (-10+4, -2+6)/2 = (-6, 4)/2

A = (-3, 2)

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b) The radius is the distance from the center to one end of the diameter. The distance formula can be used to find that.

r = √((x2 -x1)² +(y2 -y1)²) = √((4-(-3))² +(6 -2)²) = √(49+16)

r = √65

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c) The circle centered at (h, k) with radius r has formula ...

(x -h)² +(y -k)² = r²

So the formula for this circle is ...

(x +3)² +(y -2)² = 65