Question

Which conic section is represented by the equation shown below?
-4x^2-9x+4y^2+8x=16

Answer 1

would this be a hyperbola, parabola, circle, or ellipse?

Answer 2

@ranga

Answer 3

-4x^2-9x+4y^2+8x=16

Does the equation have both x^2 and y^2 terms?
If yes, then it is NOT a parabola.
Here both x^2 and y^2 are in the equation. Therefore, it is not a parabola.

Do the coefficients of x^2 and y^2 terms have the same sign?
If yes then it is either an ellipse or a circle.
It is a circle if the coefficients of x^2 and y^2 are the same
(same sign, same numbers)
It is an ellipse if the coefficients of x^2 and y^2 are NOT the same
(same sign, but different numbers

If the coefficients of x^2 and y^2 terms have opposite signs then it is a hyperbola.

Here the coefficients of x^2 and y^2 are: -4 and +4.
They have opposite signs and therefore it is a hyperbola.

Answer 4

thank you :)

Answer 5

you are welcome. :)