SOLUTION: What type of conic section is this 6x²+9y²-24x-54y+105=0

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Question 1181515: What type of conic section is this 6x²+9y²-24x-54y+105=0
Found 2 solutions by Solver92311, ikleyn:
Answer by Solver92311(821) About Me  (Show Source):
You can put this solution on YOUR website!


Has both and terms: Not a parabola

Coefficients on the squared terms equal: Circle

Coefficients on the squared terms unequal but same sign: Ellipse

Coefficients on the squared terms opposite signs: Hyperbola

John

My calculator said it, I believe it, that settles it

From
I > Ø

Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!
.

John listed the cases,  but forgot to add one hidden case  (a huge underwater stone).


For cases of a circle or an ellipse,  it may happen after transformations,  that the constant
in the right side is less than zero,  while the left side is strictly positive.


In this case the set of points is  EMPTY :   there is  NO  any figure.