ohohaye
  • ohohaye
Write the equation of the conic section with the given properties A hyperbola with vertices (0,-6) and (0,6) and asymptotes y=3/4x and y=-3/4x
Mathematics
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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ohohaye
  • ohohaye
@jim_thompson5910
jim_thompson5910
  • jim_thompson5910
let me think
jim_thompson5910
  • jim_thompson5910
how far did you get with this?

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More answers

ohohaye
  • ohohaye
Nowhere
jim_thompson5910
  • jim_thompson5910
what is the midpoint of (0,6) and (0,-6) ?
ohohaye
  • ohohaye
0
ohohaye
  • ohohaye
Or (0,0)
jim_thompson5910
  • jim_thompson5910
(0,0) yes
jim_thompson5910
  • jim_thompson5910
what is the distance from (0,0) to (0,6)
ohohaye
  • ohohaye
6
jim_thompson5910
  • jim_thompson5910
so a = 6 'a' is the distance from the center (0,0) to either vertex
jim_thompson5910
  • jim_thompson5910
to find b, we need to solve this equation a/b = 3/4
jim_thompson5910
  • jim_thompson5910
a = 6, so a/b = 3/4 6/b = 3/4 what is the value of b?
ohohaye
  • ohohaye
7?
jim_thompson5910
  • jim_thompson5910
6/b = 3/4 6*4 = b*3 ... cross multiply 24 = 3b 3b = 24 b = ?????
ohohaye
  • ohohaye
8
jim_thompson5910
  • jim_thompson5910
b = 8 is correct
jim_thompson5910
  • jim_thompson5910
(h,k) is the center, so (h,k) = (0,0) h = 0 and k = 0
jim_thompson5910
  • jim_thompson5910
a = 6 b = 8 h = 0 k = 0 plug those values into \[\Large \frac{(y-k)^2}{a^2} - \frac{(x-h)^2}{b^2} = 1\]
ohohaye
  • ohohaye
\[\frac{ (y-0)^2 }{ 6^2 }-\frac{ (x-0)^2 }{ 8^2 }\]
ohohaye
  • ohohaye
=1
jim_thompson5910
  • jim_thompson5910
yes
ohohaye
  • ohohaye
Ok, and would I do the same thing for the Ellipse except with the Ellipse formula?
jim_thompson5910
  • jim_thompson5910
ellipses don't have asymptotes though
ohohaye
  • ohohaye
then how would I solve it if it were an Ellipse and it asked for a minor or major axis?
jim_thompson5910
  • jim_thompson5910
I'd have to see the full problem
ohohaye
  • ohohaye
Like this: Write the equation of the conic section with the given properties an Ellipse with vertices (0,-5) and (0,5) and a minor axis of length 8
jim_thompson5910
  • jim_thompson5910
what is the distance from (0,-5) to (0,5) ?
ohohaye
  • ohohaye
10?
jim_thompson5910
  • jim_thompson5910
yes, half of this distance is 5 half of the minor axis (8) is 4 so for \[\Large \frac{(x-h)^2}{a^2} + \frac{(y-k)^2}{b^2} = 1\] we know that h = 0 k = 0 a = 4 b = 5
ohohaye
  • ohohaye
\[\frac{ (x-0)^2 }{ 4^2 }+\frac{ (y-0)^2 }{ 5^2 }=1\]
jim_thompson5910
  • jim_thompson5910
yeah
ohohaye
  • ohohaye
Ok, thank you
jim_thompson5910
  • jim_thompson5910
no problem

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