How do you write and graph the equation of a circle with center at (5, 4) and a radius of #4/7#?

2 Answers
Sep 28, 2017

See a solution process below:

Explanation:

The equation for a circle is:

#(x - color(red)(a))^2 + (y - color(red)(b))^2 = color(blue)(r)^2#

Where #(color(red)(a), color(red)(b))# is the center of the circle and #color(blue)(r)# is the radius of the circle.

Substituting the values from the problem gives:

#(x - color(red)(5))^2 + (y - color(red)(4))^2 = (color(blue)(4/7))^2#

#(x - color(red)(5))^2 + (y - color(red)(4))^2 = 16/49#

graph{(x-5)^2+(y-4)^2-16/49=0 [-1, 13, -1, 6]}

Mar 29, 2018

#(x-5)^2+(y-4)^2=16/49#

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)=(5,4)" and "r=4/7#

#(x-5)^2+(y-4)^2=16/49larrcolor(red)"is the equation of the circle"#
graph{(x-5)^2+(y-4)^2-16/49=0 [-10, 10, -5, 5]}