equation for a circle with a diameter that has endpoints at (2, –5) and (8, –9)

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10-01-2018
Mathematics

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equation for a circle with a diameter that has endpoints at (2, –5) and (8, –9)

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carlosego carlosego · Answer 1 · 2018-01-10T18:50:44+01:00

The standard form for the equation of a circle is :

(x−h)^2+(y−k)^2=r2 ----------- EQ(1)
where handk are the x and y coordinates of the center of the circle and r is the radius.
The center of the circle is the midpoint of the diameter.

So the midpoint of the diameter with endpoints at (2,-5)and(8,-9) is :

((2+(8))/2,(-5+(-9))/2)=(5,-7)

So the point (5,-7) is the center of the circle.

Now, use the distance formula to find the radius of the circle:

r^2=(2−(5))^2+(-5−(-7))^2=9+4=13

⇒r=√13

Subtituting h=5, k=-7 and r=√13 into EQ(1) gives :

(x-5)^2+(y+7)^2=13