How do you write the equation of the circle with end points of the circle are (-3, 5) (9, -7)?

1 Answer
Jul 22, 2017

Answer:

#(x-3)^2+(y+1)^2=72#

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 the radius.

#"the centre of the circle is at the midpoint of the 2 given"#
#"points and the radius is the distance from the centre to"#
#"either of the 2 points"#

#"midpoint "=[1/2(-3+9),1/2(5-7)]=(3,-1)#

#"calculate distance between "(3,-1)" and "(-3,5)#

#"using the "color(blue)"distance formula"#

#r=sqrt((-3-3)^2+(5+1)^2)=sqrt72#

#"using " (a,b)=(3,-1)" and "r=sqrt72#

#rArr(x-3)^2+(y+1)^2=72" is the equation"#