Mathematics, 31.07.2019 09:30, ScardeySpider

One focus of a hyperbola is located at (−1, 7). one vertex of the hyperbola is located at (−1, 5). the center is (−1, −3). what is the equation of the hyperbola?

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So, if we plot those points, we'll end up with the picture below.

now, notice, the hyperbola is a vertical one, thus it has a vertical traverse axis, and since we know the center is at -1, -3, from there upwards straight up to the vertex at -1, 5, is 8 units, therefore, the "a" component is 8.

we also know that the distance from the center up to the focus point at -1,7 is 10 units, as you can see in the picture, therefore the distance "c" is 10.

since the hyperbola is a vertical one, the fraction with the positive sign, is the one with the "y" variable, and the equation for it will be like the one you see there in the picture, thus

$\bf \textit{hyperbolas, vertical traverse axis }\\\\
\cfrac{(y- k)^2}{ a^2}-\cfrac{(x- h)^2}{ b^2}=1
\qquad 
\begin{cases}
center\ ( h, k)\\
vertices\ ( h, k\pm a)\\
c=\textit{distance from}\\
\qquad \textit{center to foci}\\
\qquad \sqrt{ a ^2+ b ^2}
\end{cases}\\\\
-------------------------------$

$\bf \begin{cases}
a=8\\
c=10
\end{cases}\implies c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b
\\\\\\
\sqrt{10^2-8^2}=b\implies \sqrt{100-64}=b\implies 6=b
\\\\\\
\textit{and since we know the center is at }(-1,-3)
\\\\\\
\cfrac{[y-(-3)]^2}{ 10^2}-\cfrac{[x-(-1)]^2}{ 6^2}=1\implies \cfrac{(y+3)^2}{100}-\cfrac{(x+1)^2}{36}=1$

One focus of a hyperbola is located at (−1, 7). one vertex of the hyperbola is located at (−1, 5). t

One focus of a hyperbola is located at (−1, 7). one vertex of the hyperbola is located at (−1, 5). t

answered: Guest

If you need an equation, it would be y=2x+8, y would be how long it grew, x being weeks.if you need how long he was asleep, it would be 4 weeks if he started with no beard, the equation would be x=8÷2if he did have a beard before hand, the equation would be 2w+x=8

answered: Guest

the most boring thing ever written

step-by-step explanation:

i am writing something. yes, i plan to make it the most boring thing ever written. i go to the store. a car is parked. many cars are parked or moving. some are blue. some are tan. they have windows. in the store, there are items for sale. these include such things as soap, detergent, magazines, and lettuce. you can enhance your life with these products. soap can be used for bathing, be it in a bathtub or in a shower. apply the soap to your body and rinse. detergent is used to wash clothes. place your dirty clothes into a washing machine and add some detergent as directed on the box. select the appropriate settings on your washing machine and you should be ready to begin. magazines are stapled reading material made with glossy paper, and they cover a wide variety of topics, ranging from news and politics to business and stock market information. some magazines are concerned with more recreational topics, like sports card collecting or different kinds of hairstyles. lettuce is a vegetable.