The Parabola as a Locus Worksheet with Answer Key

What's on the worksheet

1. Give the vertex, focus and directrix of each parabola, and say which way it opens.
   y^2 = 12xx^2 = -6y(x + 3)^2 = 8(y - 1)(y - 2)^2 = -12(x + 1)5x^2 = 2y
2. A parabola has vertex (−4, 4) and focus (−4, 7).
3. For one number r, the parabola y² + 6y - 8x + r = 0 has its focus on the y-axis.
4. Write y = 14x² + x + 3 in the form (x - h)² = 4p(y - k).
5. A parabola has vertex (2, −1) and a horizontal axis, and it passes through the point (6, 3).
6. Use the definition of a parabola to find every point of x² = 8y that is 10 units from its focus.
7. Two parabolas share the focus (2, 1).