# 11.5E: Exercises

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### Practice Makes Perfect

##### Exercise $$\PageIndex{13}$$ Graph a Hyperbola with Center at $$(0,0)$$

In the following exercises, graph.

1. $$\frac{x^{2}}{9}-\frac{y^{2}}{4}=1$$
2. $$\frac{x^{2}}{25}-\frac{y^{2}}{9}=1$$
3. $$\frac{x^{2}}{16}-\frac{y^{2}}{25}=1$$
4. $$\frac{x^{2}}{9}-\frac{y^{2}}{36}=1$$
5. $$\frac{y^{2}}{25}-\frac{x^{2}}{4}=1$$
6. $$\frac{y^{2}}{36}-\frac{x^{2}}{16}=1$$
7. $$16 y^{2}-9 x^{2}=144$$
8. $$25 y^{2}-9 x^{2}=225$$
9. $$4 y^{2}-9 x^{2}=36$$
10. $$16 y^{2}-25 x^{2}=400$$
11. $$4 x^{2}-16 y^{2}=64$$
12. $$9 x^{2}-4 y^{2}=36$$

1.

3.

5.

7.

9.

11.

##### Exercise $$\PageIndex{14}$$ Graph a Hyperbola with Center at $$(h,k)$$

In the following exercises, graph.

1. $$\frac{(x-1)^{2}}{16}-\frac{(y-3)^{2}}{4}=1$$
2. $$\frac{(x-2)^{2}}{4}-\frac{(y-3)^{2}}{16}=1$$
3. $$\frac{(y-4)^{2}}{9}-\frac{(x-2)^{2}}{25}=1$$
4. $$\frac{(y-1)^{2}}{25}-\frac{(x-4)^{2}}{16}=1$$
5. $$\frac{(y+4)^{2}}{25}-\frac{(x+1)^{2}}{36}=1$$
6. $$\frac{(y+1)^{2}}{16}-\frac{(x+1)^{2}}{4}=1$$
7. $$\frac{(y-4)^{2}}{16}-\frac{(x+1)^{2}}{25}=1$$
8. $$\frac{(y+3)^{2}}{16}-\frac{(x-3)^{2}}{36}=1$$
9. $$\frac{(x-3)^{2}}{25}-\frac{(y+2)^{2}}{9}=1$$
10. $$\frac{(x+2)^{2}}{4}-\frac{(y-1)^{2}}{9}=1$$

1.

3.

5.

7.

9.

##### Exercise $$\PageIndex{15}$$ Graph a Hyperbola with Center at $$(h,k)$$

In the following exercises,

1. Write the equation in standard form and
2. Graph.
1. $$9 x^{2}-4 y^{2}-18 x+8 y-31=0$$
2. $$16 x^{2}-4 y^{2}+64 x-24 y-36=0$$
3. $$y^{2}-x^{2}-4 y+2 x-6=0$$
4. $$4 y^{2}-16 x^{2}-24 y+96 x-172=0$$
5. $$9 y^{2}-x^{2}+18 y-4 x-4=0$$

1.

1. $$\frac{(x-1)^{2}}{4}-\frac{(y-1)^{2}}{9}=1$$

3.

1. $$\frac{(y-2)^{2}}{9}-\frac{(x-1)^{2}}{9}=1$$

5.

1. $$\frac{(y+1)^{2}}{1}-\frac{(x+2)^{2}}{9}=1$$
##### Exercise $$\PageIndex{16}$$ Identify the Graph of each Equation as a Circle, Parabola, Ellipse, or Hyperbola

In the following exercises, identify the type of graph.

1. $$x=-y^{2}-2 y+3$$
2. $$9 y^{2}-x^{2}+18 y-4 x-4=0$$
3. $$9 x^{2}+25 y^{2}=225$$
4. $$x^{2}+y^{2}-4 x+10 y-7=0$$
1. $$x=-2 y^{2}-12 y-16$$
2. $$x^{2}+y^{2}=9$$
3. $$16 x^{2}-4 y^{2}+64 x-24 y-36=0$$
4. $$16 x^{2}+36 y^{2}=576$$

2.

1. Parabola
2. Circle
3. Hyperbola
4. Ellipse
##### Exercise $$\PageIndex{17}$$ Mixed Practice

In the following exercises, graph each equation.

1. $$\frac{(y-3)^{2}}{9}-\frac{(x+2)^{2}}{16}=1$$
2. $$x^{2}+y^{2}-4 x+10 y-7=0$$
3. $$y=(x-1)^{2}+2$$
4. $$\frac{x^{2}}{9}+\frac{y^{2}}{25}=1$$
5. $$(x+2)^{2}+(y-5)^{2}=4$$
6. $$9 x^{2}-4 y^{2}+54 x+8 y+41=0$$
7. $$x=-y^{2}-2 y+3$$
8. $$16 x^{2}+9 y^{2}=144$$

2.

4.

6.

8.

##### Exercise $$\PageIndex{18}$$ Writing Exercises
1. In your own words, define a hyperbola and write the equation of a hyperbola centered at the origin in standard form. Draw a sketch of the hyperbola labeling the center, vertices, and asymptotes.
2. Explain in your own words how to create and use the rectangle that helps graph a hyperbola.
3. Compare and contrast the graphs of the equations $$\frac{x^{2}}{4}-\frac{y^{2}}{9}=1$$ and $$\frac{y^{2}}{9}-\frac{x^{2}}{4}=1$$.
4. Explain in your own words, how to distinguish the equation of an ellipse with the equation of a hyperbola.