Relationship between two complex numbers
Given that where and , prove that:
a) if u varies but v is constant, then the locus of is a parabola,
b) if v varies and u is constant, then the locus of P is again a parabola.
Show that these two parabolas have the same axis and focus.
From the relation:
Which is the parametric equation for a parabola.
When u varies, the parabola has focus and axis .
When v varies, the parabola has focus and axis .
The parabolas face in opposite directions, and both cross the y-axis, assuming that the constants are greater than 0. My problem is how do I show that they have the same focus. They do have the same axis.