How do you find the equation of the circle given center at the (10, 5) and a radius of 11?

2 Answers
Mar 20, 2018

Answer:

#(x-10)^2+(y-5)^2=121#

Explanation:

#"the standard form of the equation of a circle 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)=(10,5)" and "r=11#

#rArr(x-10)^2+(y-5)^2=121larrcolor(red)"equation of circle"#

Mar 20, 2018

Answer:

#x^2+y^2-20x-10y-4=0#

Explanation:

To find the equation of a circle whose radius and center has been given, we have a formula,
#(x-h)^2+(y-k)^2=r^2#
where, #h# and #k# are the x-coordinate and y-coordinate of the center and #r# is the radius.
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So,
#(x-10)^2+(y-5)^2=11^2#
#x^2-20x+100+y^2-10y+25=121#
#x^2+y^2-20x-10y-4=0#

Hope this helps :)