What is the equation of a circle with a center of (-5,8) and a radius of 6?

2 Answers
Binayaka C.
Mar 30, 2018

Equation of circle is #x^2+y^2+10x-16y +53=0 #

Explanation:

The center-radius form of the circle equation is

#(x – h)^2 + (y – k)^2 = r^2#, with the center being at the point

#(h=-5, k=8)# and the radius being #r=6#.

Hence equation of circle is #(x + 5)^2 + (y-8)^2 = 6^2# or

#x^2+10x +25 + y^2-16y+64 = 36 # or

#x^2+y^2+10x-16y +25+64-36=0 #

#x^2+y^2+10x-16y +53=0 #.

Equation of circle is #x^2+y^2+10x-16y +53=0 #

graph{x^2+y^2+10x-16y+53=0 [-40, 40, -20, 20]} [Ans]

Jim G.
Mar 30, 2018

#(x+5)^2+(y-8)^2=36#

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 "(a,b)=(-5,8)" and "r=6#

#(x-(-5))^2+(y-8)^2=6^2#

#rArr(x+5)^2+(y-8)^2=36larrcolor(blue)"is the equation"#

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