4. Consider the polar equation \ (r (3-k\cos \theta )=4\text {.}\) For what values of the constant \ (k\) is this conic section an ellipse? Now assume that \ (k\) has the value in the middle of the ...

In this 3-part activity, students use paper-folding and an interactive computer sketch to develop the equation of a parabola given the focus and directrix.

(a) From r = 1 2 1 − 2cosθ we see that the eccentricity is e = 2 and the equation therefore represents a hyperbola. From ed = 1 2 we conclude that the directrix is x = − 1 4.