Is 3x^2 - 5y^2 + 4x + y - 10 = 0 an hyperbola?

Conics flow-chart:

. . .Start with an equation having all the variable terms
. . .gathered together on one side of the "equals" sign.

. . .Does the equation have two squared terms?
. . . . .No: It's a parabola.
. . . . .Yes: Continue...

. . . . .Do the squared terms have the same sign?
. . . . . . .No: It's an hyperbola.
. . . . . . .Yes: Continue...

. . . . . . .Do the squared terms have the same coefficient?
. . . . . . . . .No: It's an ellipse.
. . . . . . . . .Yes: It's a circle.

Find where your equation fits in the chart.

Eliz.
 
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