Conic Sections Exercises

Find the vertex, focus, directrix, and line of symmetry of y = 8(x – 5)²+ 2.

Hint

p equals 2, and the parabola opens up.

Find the vertex, focus, directrix, and line of symmetry for (y + 5)² = -8(x + 4).

Hint

The y term is squared, and p is negative, so this parabola opens left.

Graph (y – 2)² = 3(x + 1).

Hint

The y term is squared, and p is positive, so this parabola opens right. The focus will be to the right of the vertex.

Convert y² + 6y + 4x + 1 = 0 to the conic form of a parabola.

Hint

-4x = (y² + 6y + 9) + 1 – 9

Convert y = x² – x – 1 to the conic form of a parabola.

Hint

y = (x² – x + ¼) – 1 – ¼