SOLUTION: show that 2x ^ 2 + 3y^2 - x + 2y + 1 = 0 is a circle

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: show that 2x ^ 2 + 3y^2 - x + 2y + 1 = 0 is a circle      Log On


   

Question 1207523: show that 2x ^ 2 + 3y^2 - x + 2y + 1 = 0 is a circle
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!


a circle formula is
%28x-h%29%5E2+%2B%28y-k%29%5E2=r%5E2

so, complete squares in given equation

2x%5E2+%2B+3y%5E2+-+x+%2B+2y+%2B+1+=0
%282x%5E2-x%29+%2B+%283y%5E2+%2B+2y%29++=-1
2%28x%5E2-x%2F2%29%2B3%28y%5E2%2B2y%2F3%29=-1
2%28x%5E2-%281%2F2%29x%2Bb%5E2%29-2b%5E2%2B3%28y%5E2%2B%282%2F3%29y%2Bb%5E2%29-3b%5E2=-1
for x+part b=%281%2F2%29%2F2=1%2F4
for y part b=%282%2F3%29%2F2=1%2F3


2%28x-1%2F4%29%5E2-2%281%2F16%29%2B3%28y%2B1%2F3%29%5E2-3%281%2F9%29=-1
2%28x-1%2F4%29%5E2-1%2F8%2B3%28y%2B1%2F3%29%5E2-1%2F3=-1
2%28x-1%2F4%29%5E2%2B3%28y%2B1%2F3%29%5E2=-1%2B1%2F8%2B1%2F3
2%28x-1%2F4%29%5E2%2B3%28y%2B1%2F3%29%5E2=-13%2F24
as you can see, we cannot get a formula of a circle which means given equation is NOT a circle


Answer by ikleyn(52818) About Me  (Show Source):
You can put this solution on YOUR website!
.

Wrong formulation.

Having different coefficients at x^2 and y^2, this equation CAN NOT be an equation of a circle.

After transformations, this equation defines the EMPTY set of points.