Question 244978
to graph this circle, you need to solve for y.


solving for y gets you:


y = +/- sqrt (-x^2+4x+5) - 5


graph looks like this:


{{{graph(600,600,-10,10,-10,10,sqrt(-x^2+4x+5)-5,-sqrt(-x^2+4x+5)-5)}}}


the center of this circle looks like it might be (x,y) = (2,-5).


in order to know for sure, we have to transform the equation into the proper form.


the proper form is (x-h)^2 + (y-k)^2 = r^2

where (h,k) is the center of the circle.


the original equation is:


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


move the terms around until you have all the x's together and all the y's together.


move the constant term to the right side of the equation.


you get:


(x^2 - 4x) + (y^2 + 10y) = -20


complete the squares for both of these to get:


(x-2)^2 + (y+5)^2 = -20 + 4 + 25


this becomes:


(x-2)^2 + (y+5)^2 = 9


The center of the circle is at (x,y) = (2,-5) and the radius of the circle is 3.


the graph confirms that.