What is the equation for this circle based on this problem? center (-4, -3) Point (2,2)

1 Answer
Jim G.
May 9, 2018

#(x+4)^2+(y+3)^2=61#

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 "=(-4,-3)#

#"the radius is the distance from the centre to the point "#
#"on the circle "(2,2)#

#"calculate r using 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)=(-4,-3)" and "(x_2,y_2)=(2,2)#

#r=sqrt((2+4)^2+(2+3)^2)=sqrt(36+25)=sqrt61#

#"substituting these values into the equation"#

#(x-(-4))^2+(y-(-3))^2=(sqrt61)^2#

#rArr(x+4)^2+(y+3)^2=61larrcolor(red)"equation of circle"#

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