Determine the equation of a circle if (3,2) and (-1,6) are the end points of a diameter of the circle.
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Using diameter form,the equation of the circle having A(−3,−2) and B(−3,−5) as the end points of a diameter is
(x−(−3))(x−(−3))+(y−(−2))(y−(−5))=0
⇒(x+3)(x+3)+(y+2)(y+5)=0
⇒x
2
+6x+9+y
2
+5y+2y+10=0
⇒x
2
+y
2
+6x+7y+19=0 is the required equation of the circle.
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