What is the standard form of the equation of a circle with r = 5; (h, k) = (-5, 2)?

1 Answer
Dec 9, 2015

Answer:

#(x+5)^2+(y-2)^2=25#

Explanation:

The standard form of the equation of a circle of radius #r# centered at the point #(h,k)# is #(x-h)^2+(y-k)^2=r^2#.

This equation is reflecting the fact that such a circle consists of all points in the plane that are distance #r# from #(h,k)#. If a point #P# has rectangular coordinates #(x,y)#, then the distance between #P# and #(h,k)# is given by the distance formula #sqrt{(x-h)^2+(y-k)^2}# (which itself comes from the Pythagorean Theorem).

Setting that equal to #r# and squaring both sides gives the equation #(x-h)^2+(y-k)^2=r^2#.