Chapter 21

1. Points: $(4, - 1), (6, 3)$
1. $d = \sqrt{{(6 - 4)}^{2} + {[3 - (- 1)]}^{2}} = \sqrt{4 + 16} = 2 \sqrt{5}$
2. Between points $m = \frac{3 - (- 1)}{6 - 4} = 2;$ perp. line, $m = - \frac{1}{2}$
2. $\begin{array}{rcl} 2 (x^{2} + x) & = & 1 - y^{2} \\ 2 x^{2} + y^{2} + 2 x - 1 & = & 0 \end{array}$

$A \neq C$ (same sign)

$B = 0 :$ ellipse
3. $\begin{array}{rcl} 4 x - 2 y + 5 & = & 0 \\ y & = & 2 x + \frac{5}{2} \\ m & = & 2 b = \frac{5}{2} \end{array}$
4. $\begin{array}{rcl} x^{2} & = & 2 x - y^{2} \\ x^{2} + y^{2} & = & 2 x \\ r^{2} & = & 2 r \cos θ \\ r & = & 2 \cos θ \end{array}$
5. $\begin{array}{l} x^{2} = - 12 y \\ 4 p = - 12, p = - 3 \\ V (0, 0) F (0, - 3) \end{array}$
6. Center $(- 1, 2); h = - 1, k = 2$

$\begin{array}{l} \begin{array}{rcl} r & = & \sqrt{{(2 + 1)}^{2} + {(3 - 2)}^{2}} \\ = & \sqrt{10} \end{array} \\ {(x + 1)}^{2} + {(y - 2)}^{2} = 10 \end{array}$

or

$x^{2} + y^{2} + 2 x - 4 y - 5 = 0$
7. $m = \frac{- 2 - 1}{2 + 4} = - \frac{1}{2}$

$\begin{array}{rcl} y - 1 & = & - 1 \end{array}$

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Basic Technical Mathematics, 11th Edition by Allyn J. Washington, Richard Evans