"write the equation for the conic section if the cone is centered at (0,0), the major axis is 10 units, and the minor axis is 6 units. (there is more than one correct answer.)"

teach said because it didn't want one over the other that we could pick one. i picked the horizontal form.

(x^2/a^2)+(y^2/b^2)=1

i stuck the major in for a and the minor for b, so what do i do next?

1- is the product of two rational numbers irrational or rational? first, make a hypothesis by multiplying two rational numbers. then, use variables such as x=a/b and y=c/d and the closure property of integers to prove your hypothesis. 2- what do you think the product of a nonzero rational number and an irrational number is? is it rational or irrational? make use of variables, the closure property of integers, and possibly a proof by contradiction to prove your hypothesis. 3- why do we have to specify that the rational number must be nonzero when we determine what the product of a nonzero rational number and an irrational number is? if the rational number were 0, would it give us the same result we found in part b?