16. Parametric Equations & Polar Coordinates

Parabolas

Exercises 9-16 give equations of parabolas. Find each parabola's focus and directrix. Then sketch the parabola. Include the focus and directrix in your sketch.

x = −3y²

Parabolas

Exercises 9-16 give equations of parabolas. Find each parabola's focus and directrix. Then sketch the parabola. Include the focus and directrix in your sketch.

x² = 6y

Shifting Conic Sections

You may wish to review Section 1.2 before solving Exercises 39-56.

Exercises 53-56 give equations for hyperbolas and tell how many units up or down and to the right or left each hyperbola is to be shifted. Find an equation for the new hyperbola, and find the new center, foci, vertices, and asymptotes.

x²/4 − y²/5 = 1, right 2, up 2

Hyperbolas

Exercises 27-34 give equations for hyperbolas. Put each equation in standard form and find the hyperbola's asymptotes. Then sketch the hyperbola. Include the asymptotes and foci in your sketch.

8x² − 2y² = 16

Describe the hyperbola $\(\frac{\left(x+2\right)^2}{9}\)-\(\frac{\left(y-4\right)^2}{16}\)=1$.

Sketch a graph of the circle based on the following equation: $\(\left\)(x-2\(\right\))^2+\(\left\)(y+3\(\right\))^2=1$