Question

Identify and draw the following graph: 2x^2 + y^2 - 4x + 4y + 6 = 0 Completed the square, and I got: 2(x+1)^2 + (y+2)^2 = 0 I realized that the number in front of the bracket won't go away, so I divided everything by 2. (x+1)^2 + (y + 2)^2/2 = 0 So it is an ellipse, but not with a radius of 1. So I searched this case up and found that is a "degenerate ellipse", but couldn't find any good procedure for drawing this. How would you go about with drawing this?

Answer 1

that is because you have two perfect squares on the left, and 0 on the right

Answer 2

so the left hand side can only be 0 if x = -1 and y = -2
therefore the "graph" is the point (-1,-2)

Answer 3

not much of a graph really, just a point in the plane

Answer 4

How do you get that x and y value?