find the equation of a circle with A (2,-3) and B (-3,5) as endpoints of a diameter
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distance between A and B=√(-3-2)^2 +(5+3)^2
=√(-5)^2+(8)^2
=√25+64
=√89 unit
diameter =√89 unit
radius=√89/2
coordinate of origin=【(2-3)/2. ,(5-3)/2】
( -1/2,1)
required equation of circle
=(x+1/2)^2 +( y-1)^2=(√89/2)^2
=x^2+1/4+x +y^2+1-2y=89/4
=(4x^2+4x+1 +4y^2+4-8y)/4=89/4
=4x^2+4x +4y^2-8y+5=89
=4x^2+4x+4y^2-8y=84
=√(-5)^2+(8)^2
=√25+64
=√89 unit
diameter =√89 unit
radius=√89/2
coordinate of origin=【(2-3)/2. ,(5-3)/2】
( -1/2,1)
required equation of circle
=(x+1/2)^2 +( y-1)^2=(√89/2)^2
=x^2+1/4+x +y^2+1-2y=89/4
=(4x^2+4x+1 +4y^2+4-8y)/4=89/4
=4x^2+4x +4y^2-8y+5=89
=4x^2+4x+4y^2-8y=84
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