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 have identical coefficients, it is a circle.)