Hello, rednest!
The point is on the ellipse with equation:
The line through parallel to the -axis meets the -axis at
The point is on the line produced so that
Find, in cartesian form, an equation of the locus of , as varies.Code:| * * * * | * P * | o - * | * | * : | * | : y * | * θ | * : ----*-------------+----------+--*---- * | X| * : | | : * | | * : * | * : 2y * | * | : * * * | : | | : | | : | o - | Q
After all that sketching and a lot of thinking, it turns out that
. . the equations for Q are: .
Eliminate the parameter: .
. . . . . . . . . . . . Square: .
Therefore: .