Use the Discriminant to Determine If the Graph of the Equation

question 17

Essay

Use the discriminant to determine if the graph of the equation, $13 x ^ { 2 } + 6 \sqrt { 3 } x y + 7 y ^ { 2 } = 64$ is a parabola, an ellipse or a hyperbola, then use a rotation of axes to eliminate the $x y$ - term, and sketch the graph.

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Definitions:

Lens

In optics, a lens is a transparent device that refracts or bends light rays to focus them, used in glasses, cameras, and various instruments for magnification or correction.

Fovea

A tiny indent in the eye's retina that features the greatest visual sharpness because of a high density of cones.

Retina

The light-sensitive layer of tissue at the back of the inner eye, converting light signals into neural signals for vision.

Basilar Membrane

A structure in the cochlea of the inner ear that plays a key role in the sense of hearing by vibrating in response to sound.