x2+y2-6x-2y+18=0

Question

This question is an Algebraic function. It requires to be solved and check whether or not it gives rise to a circle. Express the question in the form: (x-k)2+(y-l)2=r2

Answer 1

x^2-6x+y^2-2y=18 is another way of writing this equation. This can be further modified:

x^2-6x+9 + y^2-2y+1=18+10; (x-3)^2+(y-1)^2=28 is of the form X^2+Y^2=a^2 which is the equation of a circle of radius a.  In this case a=sqrt(28)=2sqrt(7). The centre of the circle is (3,1) found by setting X and Y to zero and solving for x and y. Therefore, k=3,  l=1 and r=a=2sqrt(7).

Answer 2

this is a test.