Eliminate the Parameter and Find More Variables

Question

The question states:

Eliminate the parameter t from the set of parametric equations.

x = At²

y = Bt+C

where B does not equal 0, to find the alpha(α), beta(β), and delta(δ) such that x = αy²+βy+δ. Express the following in terms of A, B, and C:

α = ?

β = ?

δ = ?

I understand eliminating the parameter as much. I've done this many times. With some substitution, you would get that x = A((y-C)/B)². But I'm not sure what the second part of the question is even asking. What are these other variables and how would I go about solving for them in terms of just A, B, and C?

Answer 1

Silly proposition!

Take your eliminated equation, x = A((y - C) / B)² and multiply it our to a quaderatic.

Substitute γ for y, α for A, β for B, and δ for C.