anonymous
  • anonymous
find the equation of hyperbola. conjugate axis on the x-axis, one focus at (0, √13), equation of one directrix y= 9√13 / 13. HELP PLEASE!!!!!!! the answer is 4y^2 - 9x^2 = 36... it was stated on the book
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
Sure, do you have any idea on how to start or what the equation of a hyperbola looks like in general?
anonymous
  • anonymous
(x/a)^2 - (y/b)^2 = 1
anonymous
  • anonymous
nah. no idea.. sorry

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anonymous
  • anonymous
Yes that's right!
anonymous
  • anonymous
the equation is correct! (:
anonymous
  • anonymous
Now, we need to use the given information to deduce what a and b are.
anonymous
  • anonymous
okay okay.. :)
anonymous
  • anonymous
We have one of the focus, so we can graph this, usually not necessary though, to see in which direction the hyperbola opens up.
anonymous
  • anonymous
sqrt(13)= 3.605
anonymous
  • anonymous
|dw:1378530253315:dw|
anonymous
  • anonymous
So could you graph the point (0, sqrt(13))?
anonymous
  • anonymous
|dw:1378627196153:dw|
anonymous
  • anonymous
okay okay.. :)
anonymous
  • anonymous
??
anonymous
  • anonymous
|dw:1378530449815:dw|
anonymous
  • anonymous
yes that's what i did.. hehe.
anonymous
  • anonymous
Right, its just a point not a line.
anonymous
  • anonymous
yes.. sorry. hehe
anonymous
  • anonymous
|dw:1378530601557:dw|
anonymous
  • anonymous
Okay, try again. Remember sqrt(13)= 3.605 I graphed the conjugate axis for ya. Its the line with the pencil little bit curved as you can see, I couldn't make it a different color cus that tool is not available but anyways go ahead and tell me where the focus (0,sqrt(13)) is.
anonymous
  • anonymous
its between 3 and 4, in the y axis..
anonymous
  • anonymous
|dw:1378530971954:dw|
anonymous
  • anonymous
yes right there! (:
anonymous
  • anonymous
So with this focus we know the hyperbola opens up and down correct?
anonymous
  • anonymous
They say that the equation of the directrix is y = 0sqrt(13)/13 So where would this be?
anonymous
  • anonymous
@silverxx
anonymous
  • anonymous
the directrix is between 2 and 3, y axis.. ( y= 9√13 / 13 = 2.5)
anonymous
  • anonymous
That's right!|dw:1378531276923:dw|
anonymous
  • anonymous
That's the directrix! (:
anonymous
  • anonymous
So the vertex of that first hyperbola should be half way between the focus and the directrix, correct?
anonymous
  • anonymous
??
anonymous
  • anonymous
yes yes..
anonymous
  • anonymous
So where would the vertex be?
anonymous
  • anonymous
(0,0)?
anonymous
  • anonymous
so said yes, before to it so I thought you were sure about it?
anonymous
  • anonymous
yes im sure..
anonymous
  • anonymous
I said that the vertex would be between the directrix and the focus. Half ways between directriz. W already found the directrix and the focus. So what would be the vertex?
anonymous
  • anonymous
|dw:1378531735674:dw|
anonymous
  • anonymous
near to three..
anonymous
  • anonymous
its actually 3
anonymous
  • anonymous
|dw:1378532185640:dw|
anonymous
  • anonymous
Remember that equation is (y/a)^2 - (x/b^2=1 Does that make sense?
anonymous
  • anonymous
|dw:1378532371544:dw|
anonymous
  • anonymous
Remember that equation is (y/a)^2 - (x/b^2=1 Does that make sense?
anonymous
  • anonymous
yes...
anonymous
  • anonymous
|dw:1378532439536:dw|
anonymous
  • anonymous
We are trying to find the equation, we already have a is equal to, now we need b. Do you see that equations I put in a polygon? That's the equation we need. You gave it to me at the beginning. But we need to find the values of a and b. Correct? No we need the value for b.
anonymous
  • anonymous
|dw:1378532633022:dw|
anonymous
  • anonymous
Now any ideas how to find b?
anonymous
  • anonymous
x_x
anonymous
  • anonymous
its 2?
anonymous
  • anonymous
That's right!
anonymous
  • anonymous
Do you know how to find it? There is a formula for it
anonymous
  • anonymous
id just observed it in the graph.. maybe the pythagorean but c's not given..
anonymous
  • anonymous
|dw:1378532974473:dw| Where p is the distance from the focus to the directrix, and c is the distance from the center to the focus. We know that the center is (0,0) and the focus is (0, sqrt(13) So we can calculate all these distances. But yes, b=2. So now you can plug into the equation and you have it all done. (:
anonymous
  • anonymous
Have a good day, and good luck with your studies! (: I hope after my explanation- you've understood this clearly!
anonymous
  • anonymous
thank you so much.. im so sorry for being so.. well, you know. thank you thank you!!!
anonymous
  • anonymous
haha, your welcome! (:
anonymous
  • anonymous
how did u come up the 3 and 2 ?sorry...

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