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Points E(-2, -1) and F(3, 2) are the ends of the diameter of...

Points E(-2, -1) and F(3, 2) are the ends of the diameter of a circle. Find the equation of the circle.

A.

x2+y25x+3=0

B.

x2+y22x6y13=0

C.

x2+y2x+5y6=0

D.

x2+y2xy8=0

Correct answer is D

Given the endpoints of the diameter |EF|, the midpoint is the centre of the circle

= (2+32,1+22)=(12,12)

The radius is the distance from the centre to any point on the circle. Using (12,12) and (3,2);

r2=(312)2+(212)2=254+94

r2=344

The equation of a circle is given as:

(xa)2+(yb)2=r2, (a, b) as the centre of the circle.

=(x12)2+(y12)2=344

x2x+14+y2y+14=172

= x2y2xy8=0