anonymous
  • anonymous
Please help.medals!!! Write an equation of the hyperbola given that the center is at (2, -3), the vertices are at (2, 3) and (2, - 9), and the foci are at (2, ± 2√10).
Calculus1
  • Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
SOLVED
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga. Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus. Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
katieb
  • katieb
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
anonymous
  • anonymous
Starting with the general form of a vertical hyperbola (x term is negative & y term positive): \[1=\frac{ (y-k) ^{2}}{ a }-\frac{ (x-h) ^{2}}{ b } \] Where the center is (h,k) The vertices are at (h,k+a) & (h,k-a) And the foci are located at (h,k+c) & (h,k-c) where: \[c^{2}=a^{2}+b^{2}\] Clearly from the problem we know h=2 & k=-3 and with a little reverse engineering: (2,3)=(2,-3+6) & (2,-9)=(2,-3-6) which shows that a = 6. Since we know the foci explicitly we solve for them in much the same way: \[k \pm c = \pm 2\sqrt{10} \ \ \ \ \ \rightarrow \ \ \ \ \ \ c=\mp (3 \pm 2\ \sqrt{10}) \] At this point, I have to stop and ask you to check the problem again to make sure the values listed were correct because carrying on with my calculation I ended up with some unexpected and (presumably) incorrect results. Granted it has been a while since I have done one of these calculations so before I go any further in trying to find an error (that may not even be there) please check that the foci values listed were correct and let me know in the comments or pm me. Thank you. If you want some pictures to help in visualization might I suggest: http://sites.csn.edu/istewart/mathweb/Math127/hyperbolas/hyperbolas.htm

Looking for something else?

Not the answer you are looking for? Search for more explanations.