# Which curve is this? Analytical geometry

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#x^2-3*x*y+y^2-4*x-6*y+1=0#

Determine the curve this equation is for and the elements of the curve.

Determine the curve this equation is for and the elements of the curve.

##### 1 Answer

Jan 18, 2017

The equation:

describes an hyperbole

#### Explanation:

The equation:

is an equation of second degree in

We can determine which section by analyzing the cubic and quadratic invariant:

The cubic invariant is non null, so the curve is non degenerate.

The quadratic invariant is negative, so the curve is an hyperbole.

graph{x^2-3xy+y^2-4x-6y+1=0 [-82.2, 77.8, -43.56, 36.44]}