Identify the equation without completing the square 116x2 7

Identify the equation without completing the square, 116x^2 - 7y^2 + 97y - 344 = 0 Which type of conic section is the graph of the equation? Ellipse Circle Parabola Hyperbola

Solution

If A and C both not zero,a conic section with equation

Ax^2 +Cy^2 +Dx +Ey+F=0,is

a circle ifA*c>0,

a parabola if A *C=0,

a ellipse if A is not equal to C,A *C>0,

a hyperbola if A*C<0

We have A=116,C=-7

A*C<0

Hence the given equation is hyperbola.