Question #9691f
3 Answers
so comparing with the standard equation, the center is
The center of the circle is located at
The radius is
Explanation:
To convert the given equation of circle in the standard form, use the completing square techinque as in algebra here.
Re-write in standard form:
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"#
#"to obtain this form use "color(blue)"completing the square"#
#"on both the x and y terms"#
#"adding the squared value to complete the squares to"#
#"both sides"#
#x^2+2(-6)xcolor(red)(+36)+y^2+2(3)ycolor(magenta)(+9)=-25color(red)(+36)color(magenta)(+9)#
#(x-6)^2+(y+3)^2=20larrcolor(blue)"in standard form"#
#"with "a=6,b=-3" and "r=sqrt20=2sqrt5#
#rArr"radius "=2sqrt5" and centre "=(6,-3)#