91Ó°ÊÓ

Simplify. $$\left(3 a^{-4}\right)^{2}\left(2 a^{-5}\right)^{-1}$$

Find the center and the radius of each circle. Then graph the circle. $$x^{2}+y^{2}-8 x-84=0$$

The standard form for equations of horizontal or vertical hyperbolas centered at \((h, k)\) are as follows: $$ \frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1 $$ (Graph can't copy) $$ \frac{(y-k)^{2}}{b^{2}}-\frac{(x-h)^{2}}{a^{2}}=1 $$ The vertices are as labeled and the asymptotes are $$ y-k=\frac{b}{a}(x-h) \text { and } y-k=-\frac{b}{a}(x-h) $$ For each of the following equations of hyperbolas, complete the square, if necessary, and write in standard form. Find the center, the vertices, and the asymptotes. Then graph the hyperbola. $$ 4 x^{2}-y^{2}+24 x+4 y+28=0 $$

Simplify. $$16^{-1 / 2}$$

The standard form for equations of horizontal or vertical hyperbolas centered at \((h, k)\) are as follows: $$ \frac{(x-h)^{2}}{a^{2}}-\frac{(y-k)^{2}}{b^{2}}=1 $$ (Graph can't copy) $$ \frac{(y-k)^{2}}{b^{2}}-\frac{(x-h)^{2}}{a^{2}}=1 $$ The vertices are as labeled and the asymptotes are $$ y-k=\frac{b}{a}(x-h) \text { and } y-k=-\frac{b}{a}(x-h) $$ For each of the following equations of hyperbolas, complete the square, if necessary, and write in standard form. Find the center, the vertices, and the asymptotes. Then graph the hyperbola. $$ 4 y^{2}-25 x^{2}-8 y-100 x-196=0 $$

Simplify. $$\log 10,000$$

Find the center and the radius of each circle. Then graph the circle. $$36 x^{2}+36 y^{2}=1$$

Find the center and the radius of each circle. Then graph the circle. $$4 x^{2}+4 y^{2}=1$$

Simplify. $$i^{71}$$

Does the graph of an equation of a circle include the point that is the center? Why or why not?