Equation of a Circle with center(-2,1)and containing the point (10,-6)?

1 Answer
Jim G.
Apr 30, 2018

#(x+2)^2+(y-1)^2=193#

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"#

#"here the centre "=(-2,1)#

#"the radius is the distance from the centre to the point on"#
#"the circle "(10,-6)#

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

#r=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#

#"let "(x_1,y_1)=(-2,1)" and "(x_2,y_2)=(10,-6)#

#r=sqrt((10+2)^2+(-6-1)^2)#

#color(white)(r)=sqrt(144+49)=sqrt193#

#"substituting into the equation"#

#x-(-2))^2+(y-1)^2=(sqrt193)^2#

#(x+2)^2+(y-1)^2=193larrcolor(red)"equation of circle"#

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