Question: Conic Sections

Does any non-degenerate conic section have all of the following properties?

I. It is symmetric with respect to the origin.

II. It passes through the point (1,0).

III. It is tangent to the line y=1 at the point (-2,1).

(a) Give reasons for your answers.

Given the above problem, provide written responses to address the following points as precisely and thoroughly as possible.

A. Explain the problem in your own words.

B. What mathematical concepts learned in this module apply to this problem?

C. Explain the steps you must take to solve this problem.

D. What is the most difficult aspect of solving this problem?

E. Explain exactly what the answer means from a mathematical perspective.