anonymous
  • anonymous
Can someone help me with two questions in conic sections.
Mathematics
katieb
  • katieb
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anonymous
  • anonymous
1. What is the equation of the following graph?
1 Attachment
anonymous
  • anonymous
2. What are the foci of the following graph?
1 Attachment
xapproachesinfinity
  • xapproachesinfinity
i hyperbola has the equation \(\Large \frac{x^2}{a^2}-\frac{y^2}{b^2}=1\) so you need to find a and b

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anonymous
  • anonymous
how do I find a and b?
xapproachesinfinity
  • xapproachesinfinity
you see that box a is half way from right to left b is half way from bottom up
xapproachesinfinity
  • xapproachesinfinity
so you just take the length of that rectangle and divide into half
xapproachesinfinity
  • xapproachesinfinity
2b=8 so b=4 2a=6 so a=3
anonymous
  • anonymous
okay thank you! so the first problem is \[\frac{ x ^{2} }{ 3^{2} }-\frac{ y ^{2} }{ 4^{2} }=1\]
xapproachesinfinity
  • xapproachesinfinity
yes !
anonymous
  • anonymous
Can you also help with the 2nd problem
xapproachesinfinity
  • xapproachesinfinity
to find the foci you need to find a and b again then use b^2+c^2=a^2 c=sqrt{a^2-b^2} c is the distance from the foci to the center of that rectangle
xapproachesinfinity
  • xapproachesinfinity
that will get you the coordinates of the foci
xapproachesinfinity
  • xapproachesinfinity
you will find b and a the same way we just did
anonymous
  • anonymous
I got A=2 and B=5 is that correct?
xapproachesinfinity
  • xapproachesinfinity
yes!
anonymous
  • anonymous
okay what do I do next?
xapproachesinfinity
  • xapproachesinfinity
well i said c is the distance from center to foci so what do you think any idea
xapproachesinfinity
  • xapproachesinfinity
actually an error \(c=\sqrt{a^2+b^2}=\sqrt{29}\) the foci has coordinates (0,c)
anonymous
  • anonymous
so c=5.39?

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