SOLUTION: The hyperbola defined by the equation 3x^2 − 2y^2 + 6x − 8y = 6. And solution. Transverse Axis parallel to: x-axis or y-axis? Graph: Center of the Hyperbola: Vert

Question 1172211: The hyperbola defined by the equation 3x^2 − 2y^2 + 6x − 8y = 6.
And solution.
Transverse Axis parallel to:
x-axis or y-axis?
Graph:
Center of the Hyperbola:
Vertices of the Hyperbola:
Foci of the Hyperbola:
Equations of the Asymptotes:
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

Case 1: If the transverse axis is parallel to the x-axis (branches open right and left), then the equation is

Case 2: If the transverse axis is parallel to the y-axis (branches open up and down), then the equation is

In either equation, (h,k) is the center of the hyperbola; 2a is the length of the transverse axis, and 2b is the length of the conjugate axis.

c is the distance from the center to either focus; a, b, and c are related by

You need to complete the square in both x and y to put the given equation into one of those forms.

That is in the form of case 1: (h,k) = (-1,-2); a^2=1/3; b^2=1/2.

Transverse Axis parallel to: x-axis or y-axis? See the definition of case 1.

Graph: (I leave that to you)

Center of the Hyperbola: (h,k)

Vertices of the Hyperbola: a units to the right and left of the center

Foci of the Hyperbola: c units to the right and left of the center

Equations of the Asymptotes: the slopes are b/a and -b/a; (h,k) is a point on both asymptotes.

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