Focus and Directrix Worksheet with Answer Key

What's on the worksheet

1. Each conic has focus F and the given directrix, and passes through the point P.
   F(1, 2), directrix x = -3, P(1, 5)F(0, -2), directrix y = 2, P(4, -2)F(2, -1), directrix x = 8, P(-1, 3)F(-2, 1), directrix y = 3, P(1, 5)F(0, 0), directrix x + y = 4, P(3, 3)
2. The focus of each conic is at the pole.
   r = \dfrac{12}{4 + 3\sin\theta}r = \dfrac{10}{5 - 5\cos\theta}r = \dfrac{10}{4 - 5\sin\theta}r = \dfrac{7}{2 + 7\cos\theta}r = \dfrac{4}{6 + \cos\theta}
3. A conic has focus F(0, -3), directrix x = 9 and eccentricity e = 23.
4. A conic has its focus at the origin and eccentricity e = 13.
5. A conic has its focus F at the origin and a vertical directrix x = d.
6. A conic has its focus at the pole, eccentricity e = 32, and a directrix x = d with d > 0.