(a) Grab the directrix slider so that the directrix is x = −2. Grab the point F (the focus) and move to (4, 2). Check the box “Show Point on Parabola.” Grab point P and move it around the Cartesian Plane. Notice the distance from P to F and the distance from P to the directrix is computed. Move P to the point (4, 8). What is the distance from P to F?

(b) Continue to trace out the parabola. Notice the focus is to the right of the directrix. The parabola opens (up/down/left/right).

(c) What is the distance, a, from the focus to the vertex? What is the distance, a, from the vertex to the directrix?

(d) What are the coordinates of the vertex? Write your answer as an ordered pair.

(e) Check the box “Show Parabola.” What is the equation of the parabola? Write your answer in the form (y − k)² = 4a(x − h).

(f) Reset the interactive figure by clicking . Move the focus (point F) to (−8, 2). Change the directrix to x = 2. What are the coordinates of the vertex?

(g) Check the box “Show Point on Parabola.” Grab point P and move it around the Cartesian Plane. Notice the distance from P to F and the distance from P to the directrix is computed. Move P to the point (−8, −8). What is the distance from P to F?

(h) Continue to trace out the parabola. Notice the focus is to the left of the directrix. The parabola opens (up/down/left/right).

(i) Check the box “Show Parabola.” What is the equation of the parabola? Write your answer in the form (y − k)² = 4a(x − h).