Basic Technical Mathematics, 11th Edition

CHAPTER 21 REVIEW EXERCISES

CONCEPT CHECK EXERCISES

Determine each of the following as being either true or false. If it is false, explain why.

1. The distance between $(4\hspace{0.17em},\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}3)$ and $(3\hspace{0.17em},\hspace{0.17em}\hspace{0.17em}-\hspace{0.17em}4)$ is $\sqrt{2}\hspace{0.17em}.\hspace{0.17em}$

2. $2y\hspace{0.17em}-\hspace{0.17em}3x\hspace{0.17em}=\hspace{0.17em}6$ is a straight line with intercepts (2,0) and (0,3).

3. The center of the circle $x^2\hspace{0.17em}+\hspace{0.17em}{y}^2\hspace{0.17em}+\hspace{0.17em}2x\hspace{0.17em}+\hspace{0.17em}4y\hspace{0.17em}+\hspace{0.17em}5\hspace{0.17em}=\hspace{0.17em}0$ is (1, 2).

4. The directrix of the parabola $x^2\hspace{0.17em}=\hspace{0.17em}8y$ is the line $y\hspace{0.17em}=\hspace{0.17em}2.$

5. The vertices of the ellipse $9x^2\hspace{0.17em}+\hspace{0.17em}4y^2\hspace{0.17em}=\hspace{0.17em}36$ are (2,0) and $(\hspace{0.17em}-\hspace{0.17em}2\hspace{0.17em},\hspace{0.17em}0)\hspace{0.17em}.\hspace{0.17em}$

6. The foci of the hyperbola $9x^2\hspace{0.17em}-\hspace{0.17em}16y^2\hspace{0.17em}=\hspace{0.17em}144$ are $(\hspace{0.17em}-\hspace{0.17em}5\hspace{0.17em},\hspace{0.17em}0)$ and (5, 0).

7. The equation $x^2\hspace{0.17em}=\hspace{0.17em}{(y\hspace{0.17em}-\hspace{0.17em}1)}^2$ represents a hyperbola.

8. The equation $5x^2\hspace{0.17em}-\hspace{0.17em}8xy\hspace{0.17em}+\hspace{0.17em}5y^2\hspace{0.17em}=\hspace{0.17em}9$ represents an ellipse.

9. The rectangular equation $x\hspace{0.17em}=\hspace{0.17em}2$ represents the same curve as the polar equation $r\hspace{0.17em}=\hspace{0.17em}2\text{ sec }\theta \hspace{0.17em}.\hspace{0.17em}$

10. The graph of the polar equation ...