Little Question

[Kenpachi]

Just a little maths poblem for anyone out there

Explain why the Equation x(squared) + y(squared) + 2x + 3y + 5 = 0 does not represent a circle

Have fun!

[zaza]

Welcome to the Forums


Are you asking because you don't know, or is this for our enjoyment?


zaza

[Code Doc]

It's a warped circle. My 4-year old grandson draws lots of them with crayons and while finger painting.

Welcome to the forum!

[Logophobic]

It isn't a warped circle, either. It doesn't represent a circle, or anything else for that matter, because there are no real solutions.

Solving for x:
x² + 2x + y² + 3y + 5 = 0
x = -1 ± √(1 - (y² + 3y + 5))
such that, for x to be real:
y² + 3y + 5 ≤ 1
y² + 3y + 4 ≤ 0
-1.5 - √(-1.75) ≤ y ≤ -1.5 + √(-1.75)
y must be complex

Solving for y:
y² + 3y + x² + 2x + 5 = 0
y = (-3 ± √(9 - 4(x² + 2x + 5)))/2
such that, for y to be real:
x² + 2x + 5 ≤ 2.25
x² + 2x + 2.75 ≤ 0
-1 - √(-1.75) ≤ x ≤ -1 + √(-1.75)
x must be complex

[NotLKH]

Or:
x² + 2x + y² + 3y + 5 = 0
is easily seen to be identical to:

(x+1)² + (y+1.5)² = -1.75
therefore, x , y, either or both, must be complex, to produce a negative sum when squared, to equal -1.5.