# CHAPTER 21 REVIEW EXERCISES

# CONCEPT CHECK EXERCISES

Determine each of the following as being either ** true** or

**If it is false, explain why.**

*false.*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 $\sqrt{2}\hspace{0.17em}.\hspace{0.17em}$

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

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).

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

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

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

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

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

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

The graph of the polar equation ...

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