How do you write the equation for a circle with the endpoints of a diameter at (4, -3) and (-2, 5)?

1 Answer
Apr 25, 2018

Answer:

#(x-1)^2+(y-1)^2=25#

Explanation:

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

#"we require to find the centre and radius"#

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

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

#rArr"centre "=(1,1)#

#"using "(1,1)" and "(4,-3)#

#r=sqrt((4-1)^2+(-3-1)^2)=sqrt(9+16)=5#

#(x-1)^2+(y-1)^2=25larrcolor(red)"equation of circle"#