Find the equation to the circle such that the points #A(-3,5)# and #B(4,-2)# form the ends of a diameter?

this is all the given information.

1 Answer
Jim G.
Mar 25, 2018

#(x-1/2)^2+(y-3/2)^2=49/2#

Explanation:

#"the standard form of the equation of a circle is "#

#color(red)(bar(ul(|color(white)(2/2)color(black)((x-a)^2+(y-b)^2=r^2)color(white)(2/2)|)))#

#"where "(a,b)" are the coordinates of the centre and r is"#
#"the radius"#

#"Given the endpoints of the diameter then the centre is "#
#"at the midpoint and the radius is the distance from the "#
#"centre to one of the endpoints"#

#"the coordinates of the midpoint are the average of the"#
#"the coordinates of the endpoints"#

#"midpoint "=[1/2(-3+4),1/2(5-2)]=(1/2,3/2)#

#"to calculate the radius use the "color(blue)"distance formula"#

#•color(white)(x)r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#"let "(x_1,y_1)=(1/2,3/2)" and "(x_2,y_2)=(-3,5)#

#rArrr=sqrt((-3-1/2)^2+(5-3/2)^2#

#color(white)(r)=sqrt(49/4+49/4)=sqrt(98/4)#

#rArr(x-1/2)^2+(y-3/2)^2=(sqrt(98/4))^2#

#rArr(x-1/2)^2+(y-3/2)^2=49/2larrcolor(red)"equation of circle"#

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