anonymous
  • anonymous
Find the equation of the hyperbola given the foci are (3,5) and (13,5) and the eccentricity is 5/4
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
@welshfella
welshfella
  • welshfella
sorry guy I've forgotten this stuff.
anonymous
  • anonymous
@freckles

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More answers

freckles
  • freckles
|dw:1449432118181:dw|
freckles
  • freckles
so what does that tell you (h,k) is in: \[\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=1 \]
anonymous
  • anonymous
\[\frac{( x-8)^2 }{ a^2 }-\frac{ (y-5 )^2}{ b^2 }=1\]
freckles
  • freckles
good job on the center part... now we are left with finding a and b
anonymous
  • anonymous
\[e=\frac{ \sqrt{a^2+b^2} }{ a }\]
anonymous
  • anonymous
which gives 5/4
freckles
  • freckles
|dw:1449432650503:dw|
freckles
  • freckles
so c is given as 5
freckles
  • freckles
that is the distance between 3 and 8 and 8 and 13
freckles
  • freckles
the distance between the center and the foci
freckles
  • freckles
\[\sqrt{a^2+b^2}=5\]
freckles
  • freckles
which means a=4 and you solve that above equation for b
anonymous
  • anonymous
b^2=a^2(e^2-1) b^2=16(5/4-1) b^2=16(1/4) b^2=4
freckles
  • freckles
I got b^2=3^2 or 9
freckles
  • freckles
\[e=\frac{\sqrt{a^2+b^2}}{a} \text{ or } \frac{c}{a} \\ \text{ we have } c=5 \\ \\ \text{ so we have } \\ e=\frac{c}{a}=\frac{5}{4} \implies a=4 \\ \text{ so } \sqrt{a^2+b^2}=c \\ \sqrt{4^2+b^2}=5\]
freckles
  • freckles
and you just solve the equation for b
freckles
  • freckles
square both sides
freckles
  • freckles
oh I see a mistake in your math above
freckles
  • freckles
\[e=\frac{5}{4} \implies e^2=\frac{25}{16} \text{ not } \frac{5}{4} :p\]
freckles
  • freckles
fix that and you will be good
freckles
  • freckles
\[b^2=a^2(e^2-1) \\ b^2=4^2((\frac{5}{4})^2-1) \\ b^2=16(\frac{25}{16}-1) \\ b^2=25-16=9 \\ \]
freckles
  • freckles
do you see what I'm talking about
anonymous
  • anonymous
yes
anonymous
  • anonymous
and ur equation is \[\frac{ (x-8)^2 }{ 16 }-\frac{ (y-5)^2 }{ 9 }=1\]
freckles
  • freckles
yep
anonymous
  • anonymous
thank you
freckles
  • freckles
np

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