How do you write an equation for for circle given that the endpoints of the diameter are (-2,7) and (4,-8)?
2 Answers
Explanation:
#"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 2 endpoints"#
#"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"#
#"midpoint "=[1/2(-2+4),1/2(7-8)]=(1,-1/2)#
#"to calculate the radius use the "color(blue)"distance formula"#
#•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)#
#"let "(x_1,y-1)=(4,-8)" and "(x_2,y_2)=(1,-1/2)#
#d=sqrt((1-4)^2+(-1/2+8)^2)#
#color(white)(d)=sqrt(9+225/4)=sqrt261/2#
#(x-1)^2+(y+1/2)^2=(sqrt261/2)^2#
#rArr(x-1)^2+(y+1/2)^2=261/4larrcolor(blue)"equation of circle"#
Therefore, equation of the given circle is
Explanation:
Center coordinates
diameter /2 = radius =
Standard equation of a circle is
Therefore, equation of the given circle is