Show that the foci of $(-8t, 4t^2)$ for varying values of $t$ is a parabola.

Question

Show that the foci of $(-8t, 4t^2)$ for varying values of $t$ is a parabola.

Also, how to attempt loci questions in general?

Answer 1

$x = -8t$, and $y = 4t^2$. So: $16y = x^2$, and $y = \dfrac{1}{16}\cdot x^2$ is a parabola. Is this what you are asking?