anonymous
  • anonymous
Find an equation in standard form for the hyperbola with vertices at (0, ±6) and asymptotes at y = ±(3/7)x HELP ME :(
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@AkashdeepDeb do you know how to do this one by any chance too? :l
AkashdeepDeb
  • AkashdeepDeb
I don't know what asymptotes are. Sry.... Tag some people!! :D
anonymous
  • anonymous
alright np :D thank you!!!

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anonymous
  • anonymous
@phi @E.ali
phi
  • phi
See http://www.mathsisfun.com/geometry/hyperbola.html
phi
  • phi
If you scroll down the "Equation" it shows a hyperbola facing sideways. ) ( Your hyperbola is a "smile/frown", so you have to swap x and y in their example. That is, your hyperbola's equation is \[ \frac{y^2}{a^2} - \frac{x^2}{b^2} = 1 \]
phi
  • phi
according to the site, One vertex is at (a, 0), and the other is at (-a, 0) or in this case, where x and y are swapped One vertex is at (0,a), and the other is at (0,-a) so what is "a" for your hyperbola ?
anonymous
  • anonymous
ahh okay I see, so a is +-6 right?
phi
  • phi
yes, so if we replace a^2 with 36, the equation is \[ \frac{y^2}{36} - \frac{x^2}{b^2} = 1 \] we need to find b to finish this.
anonymous
  • anonymous
cool! wait how do we find b??
phi
  • phi
Again from the site we have (for a *sideways*) hyperbola The asymptotes are the straight lines: y = (b/a)x y = -(b/a)x we have to swap x and y for this problem (an up/down hyperbola) x = (b/a) y x = (-b/a)y they tell you y = ±(3/7)x if we look at the +, we have y = (3/7)x or, solving for x, x= (7/3)y match that equation with x= (b/a)y with a=6, we have x= (b/6)y so we have x= (7/3)y and x = (b/6)y we can set (7/3)y =(b/6)y can you find b ?
anonymous
  • anonymous
14 right? and then I'd square that under x^2 to get 196?
phi
  • phi
to solve \[ \frac{7}{3} y = \frac{b}{6} y \] first divide both sides by y. You get \[ \frac{7}{3} \cdot \frac{y}{y} = \frac{b}{6} \cdot\frac{y}{y} \\ \frac{7}{3} = \frac{b}{6}\] multiply both sides by 6
phi
  • phi
yes, b=14 and the equation is \[ \frac{y^2}{36} - \frac{x^2}{196} = 1\]
anonymous
  • anonymous
AHH THANK YOU SO MUCH :) it's a lot clearer now.
phi
  • phi
See http://www.wolframalpha.com/input/?i=%28y%2F6%29%5E2+-+%28x%2F14%29%5E2+%3D+1 where it says, Geometric Figure: hyperbola, click on Properties on the right side to get a list of properties... check that the asymptotes and vertex match with your problem

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