What are the conic sections of the following equations #x ^2 + y ^2 - 10x -2y +10= 0#?

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Answer 1 · 2016-01-08T00:21:45

This is a circle.

Complete the squares to find:

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

#=(x^2-10x+25)+(y^2-2y+1)-16#

#=(x-5)^2+(y-1)^2-4^2#

Add #4^2# to both ends and transpose to get:

#(x-5)^2+(y-1)^2 = 4^2#

which is in the form:

#(x-h)^2+(y-k)^2 = r^2#

the equation of a circle, centre #(h, k) = (5, 1)# and radius #r = 4#

graph{(x^2+y^2-10x-2y+10)((x-5)^2+(y-1)^2-0.01) = 0 [-6.59, 13.41, -3.68, 6.32]}