Application of High School level Algebra 2

Consider the following situation.

The cartoonist refers to the fact that sound or other types of waves emanating from one focal point will reflect off the inner sides of the ellipse towards the opposite focal point.

We know that an ellipse can be defined by two focal points and a constant value "a".

Let the location of the cartoon narrator's bed be the origin (0,0). We will assume that the narrator has somehow figured out the approximate location of his neighbor's bed (creepy) and that that location is 20 meters away at (0, 20).

The narrator's bedroom is not overly large, therefore, the vertex closest to his bed must be no further than one meter away. The location of this vertex will be (-1, 0).

1.) Given this information find the equation of the ellipse that the narrator built.

2.) Describe the "aberrant behavior" that would result if a spherical or parabolic reflector were used?

Critical thinking: In what situations might these types of reflectors be useful?

If you get stuck this may help.

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