Hello, jhonwashington!

3x² - 5y² + 4x + y - 10 .= .0

It is already in standard form (all terms on one side).

Since x² and y² have opposite signs, it is a hyperbola.

y² .= .-6x² + 36

Standard form: .6x² + y² - 36 .= .0

Since x² and y² have the same sign, it is an ellipse.

(Note: If x² and y² haveidenticalcoefficients, it is a circle.)