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)