Chapter 13 Test

Chapter 13 Test

Graph. Label the vertex and any intercepts.

1) $y = x^{2} - 4 x + 7$

2) $y = - {(x + 3)}^{2} + 9$

3) $x = - y^{2} + 9 y - 14$

4) $x = {(y + 1)}^{2} - 8$

Find the distance between the given points. Round to the nearest tenth if necessary.

5) $(7, - 3) and (3, 5)$

Graph the circle. Identify the center and radius of the circle.

6) ${(x + 4)}^{2} + {(y - 2)}^{2} = 25$

Find the center and radius of the circle by completing the square.

7) $x^{2} + y^{2} - 12 x - 6 y + 13 = 0$

Find the equation of the circle with the given center and radius.

8) Center $(3, - 8)$ , radius 16

Graph the ellipse. Label the center. Give the values of a and b.

9) $\frac{{(x - 4)}^{2}}{16} + \frac{{(y + 7)}^{2}}{9} = 1$

Find the center of the ellipse by completing the square. Give the values of a and b.

10) $4 x^{2} + 25 y^{2} - 64 x + 100 y + 256 = 0$

Graph the hyperbola. Label the center. Give the values of a and b.

11) $\frac{x^{2}}{16} - y^{2} = 1$

Find the equation of the conic section that has been graphed.

12)

13)

Solve the nonlinear system.

14) $\begin{array}{l} x^{2} + y^{2} = 100 \\ x + 3 y = 10 \end{array}$

15) $\begin{array}{l} x^{2} + 6 y^{2} = 49 \\ x - 2 y = 1 \end{array}$

16) $\begin{array}{l} y^{2} - x^{2} = 10 \\ y = x^{2} - 32 \end{array}$

17) $\begin{array}{l} x^{2} + 4 y^{2} = 85 \\ 3 x^{2} + 2 y^{2} = 165 \end{array}$

18) A rectangular corral has a perimeter of 340 feet and an area of 6000 square feet. Find the dimensions of the corral.