How do you graph x2+y2+4x+6y+4=0?

1 Answer
Jan 28, 2016

Sort the x terms and y terms so that they are near one another.

x2+4x+y2+6y=4

Now, complete the square for each part by adding constants. Remember that a constant added on the left side should also be added on the right to keep the equation balanced.

(x2+4x+4)+(y2+6y+9)=4+4+9

This simplifies to be

(x+2)2+(y+3)2=9

Since the standard equation of a circle with a vertex (h,k) and radius r is

(xh)2+(yk)2=r2

This tells us the circle has a vertex at (2,3) and a radius of 3.

Graph the point (2,3) and travel 3 in every direction. You should have the points:

graph{((x-1)^2+(y+3)^2-0.03)((x+5)^2+(y+3)^2-0.03)((x+2)^2+(y+3)^2-0.03)((x+2)^2+(y)^2-0.03)((x+2)^2+(y+6)^2-0.03)=0 [-10.665, 9.335, -7.76, 2.24]}

Now, draw the circle surrounding the center and passing through each exterior point:

graph{(x+2)^2+(y+3)^2=9 [-10.665, 9.335, -7.2, 2.8]}