How do you graph x2+y2+4x+6y+4=0?
1 Answer
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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
(x−h)2+(y−k)2=r2
This tells us the circle has a vertex at
Graph the point
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]}