Find the coordinates of the points of intersection of the curve with parametric equations: , where with the line
What I have tried is to substitute x and y in with those in the parametric equations, but this forms which seems hard to solve, unless a graphical calculator is used.
I too get .
I began by eliminating the parameter θ.
Equating this to the given line, we find:
Squaring both sides (and being aware that extraneous solutions may be introduced):
Collecting like terms, rearranging and factoring yields:
By substitution into (1), we see x = 0 is an extraneous solution, so we need only consider:
This equation has two real roots, one of which is extraneous. By substitution into (1), we find the only valid root is: