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Help with hyperbolas homework?
1. Find the oblique asymptotes of the hyperbola: (y-2)^2/4 - (x-1)^2/1 = 1
I know already that the answer is y=2x and y=-2x+4 but could someone explain HOW one would find that answer.
2. Find the oblique asymptotes of the hyperbola: (x-5)^2/25 - (y+1)^2/9 = 1
Again, I know the answer: y=(3/5)x-4 and y=(-3/5)x+2 but have no clue how to get those answers.
Please explain the process of doing this and it would really help if you could give a generalization using a,b, and c. Thanks! :3
1 Answer
- Anonymous8 years agoFavorite Answer
Your notation sux. We use parentheses to clarify what's what and any mistake is fatal. I guess what you meant was:
((y - 2)^2)/4 - ((x - 1)^2)/1 = 1
including extra spaces so it doesn't all run together. We are not supposed to have to guess, but what you had there simply does not meet the definition of a hyperbola. When the equation is in the form (x^2)/a^2 - (y^2)/b^2 = 1 then the slopes of the asymptotes are ±b/a.
Any general equation such as the one above is centered on the origin. If you want it centered on some point (j, k) you subtract the coordinates: ((x - j)^2)/a^2 - ((y - k)^2)/b^2 = 1. That is how we know your equation is centered at (1, 2) and the asymptotes are adjusted to pass through that point.
You don't have to memorize this page, but you should note what it contains and look it up again when you need it: https://en.wikipedia.org/wiki/Hyperbola