Mathematics, 03.07.2019 07:00 j015
Find an equation in standard form for the hyperbola with vertices at (0, ±8) and asymptotes at y = + or - 1/2 x.
Answers: 1
![\bf \textit{hyperbolas, vertical traverse axis } \\\\ \cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1 \qquad \begin{cases} center\ ( h, k)\\ vertices\ ( h, k\pm a)\\ c=\textit{distance from}\\ \qquad \textit{center to foci}\\ \qquad \sqrt{ a ^2 + b ^2}\\ asymptotes\quad y= k\pm \cfrac{a}{b}(x- h) \end{cases} \\\\[-0.35em] \rule{34em}{0.25pt}](/tpl/images/0045/5068/fb032.png)
![\bf \begin{cases} h=0\\ k=0\\ a=8 \end{cases}\implies \cfrac{(y-0)^2}{8^2}-\cfrac{(x-0)^2}{b}=1 \\\\[-0.35em] ~\dotfill\\\\ \stackrel{\textit{we know the asymptote is}}{\pm \cfrac{1}{2}x~~=~~0\pm\cfrac{8}{b}(x-0)}\implies \stackrel{\textit{using only the positive asymptote}}{\cfrac{x}{2}=\cfrac{8x}{b}\implies bx=16x}\\\\\\ b=\cfrac{16x}{x}\implies b=16 \\\\[-0.35em] ~\dotfill\\\\ \cfrac{(y-0)^2}{8^2}-\cfrac{(x-0)^2}{16^2}=1\implies \cfrac{y^2}{64}-\cfrac{x^2}{256}=1](/tpl/images/0045/5068/42999.png)
Another question on Mathematics
Mathematics, 21.06.2019 15:20
Angle mno is s rotated 180 degrees counterclockwise about the origin to form angle m’n’o’. which statement shows the measure of angle m’n’o’?
Answers: 1
Mathematics, 21.06.2019 16:30
Amuffin recipe, which yields 12 muffins, calls for cup of milk for every 1 cups of flour. the same recipe calls for cup of coconut for every cup of chopped apple. to yield a batch of 30 muffins, how much flour will be needed in the mix?
Answers: 1
Mathematics, 22.06.2019 00:00
Can someone plz me understand how to do these. plz, show work.in exercises 1-4, rewrite the expression in rational exponent form.[tex]\sqrt[4]{625} \sqrt[3]{512} (\sqrt[5]{4} )³ (\sqrt[4]{15} )^{7}\\ (\sqrt[3]{27} )^{2}[/tex]
Answers: 3
You know the right answer?
Find an equation in standard form for the hyperbola with vertices at (0, ±8) and asymptotes at y = +...
Questions
Mathematics, 17.12.2020 18:20
Mathematics, 17.12.2020 18:20
Mathematics, 17.12.2020 18:20
Mathematics, 17.12.2020 18:20
Social Studies, 17.12.2020 18:20
Mathematics, 17.12.2020 18:20
Computers and Technology, 17.12.2020 18:20
Mathematics, 17.12.2020 18:20
Chemistry, 17.12.2020 18:20
Chemistry, 17.12.2020 18:20
Mathematics, 17.12.2020 18:20
Business, 17.12.2020 18:20
Mathematics, 17.12.2020 18:20
