Answer:
Hyperbola (vertical)
Explanation:
Given conic section equation:

The general equation for any conic section is:

where A, B, C, D, E and F are constants.
If B² − 4AC < 0, if a conic exists, it will be either a circle or an ellipse.
(If A = C and B = 0, the equation represents a circle).
If B² − 4AC = 0, if a conic exists, it will be a parabola.
If B² − 4AC > 0, if a conic exists, it will be a hyperbola.
For the given equation, the coefficients of A, B and C are:
Substitute the coefficients into B² − 4AC:

As B² − 4AC > 0, the conic is a hyperbola.

To rewrite the given equation in the standard form of a hyperbola, we can complete the square.
Given equation:

Arrange the equation so all the terms with variables are on the left side and the constant is on the right side:

Factor out the coefficient of the x² term and the coefficient of the y² term:

Add the square of half the coefficient of x and y inside the parentheses of the left side, and add the distributed values to the right side:

Factor the two perfect trinomials on the left side and simplify the right side:

Divide both sides by the number of the right side so the right side equals 1:



As the y²-term is positive, the hyperbola is vertical (opening up and down).