Question

is equation x^2+y^2+24x-26y+277=0 is it a circle, ellipse ,parabola or hyperbola?

Answer 1

You have x squared and y squared - so this eliminates the parabola (only 1 variable is squared)

Circles would have to have same coefficient in front of the x square and y square - and both would have to be positive like the ellipse. Most likely the coefficient will be positive 1.

Difference between the ellipse and hyperbola is that hyperbolas have different signs - one is a positive coefficient and the other is a negative coefficient. Ellipses will have 2 positive coefficients.

Answer 2

so is it a parabola or hyperbola?

Answer 3

Parabolas only have 1 variable that is squared - this equation has an x square AND a y-square.
Hyperbolas: the Coefficients in front of the x square and y square must be different signs, 1 positive, 1 negative.
Question is: Is it an ellipse or Circle since both coeficients in front of x square and y square are both positive. What is the difference? Circles both do not have a coefficient (both are positive 1)(WINNER) and ellipses will have different coefficients.