When I run the command as follows:
Eliminate[{x^2/a^2 - y^2/b^2 == 1, y == k x + m}, y]
the result is:
m^2 + 2 k m x == -b^2 + (b^2 x^2)/a^2 - k^2 x^2 && a != 0 && b != 0
but I want to the result is like this:
b^2 + m^2 + 2 k m x + (-(b^2/a^2) + k^2) x^2 == 0
or furthermore is such as:
a^2 b^2 + a^2 m^2 + 2 a^2 k m x + (-b^2 + a^2 k^2) x^2 == 0
How to combine the similar terms after shifting the terms of the equation, and make the coefficients of the first and second terms of the quadratic equation of the univariate integer (like this `
a^2 b^2 + a^2 m^2 + 2 a^2 k m x + (-b^2 + a^2 k^2) x^2 == 0
This type answer is the best key to this question)? Thank you?
