Question

Write the equation of the asymptotes to the hyperbola with equation: x^2 - y^2 + 4x + 8y - 21 = 0

Answer 1

(x+2)^2 - (y-4)^2 - 9 = 0

Answer 2

So would y - 4 = (x+2) and y - 4 = -(x+2) be correc?

Answer 3

put the equation in standard form
(x-x0)^2/a^2 - (y-y0)^2/b^2 =1
for equations the asymptotes, let the 1 be zero, take the square root, solve for y

Answer 4

Here a = b = sqrt(9) = 3

Answer 5

\[\left( \frac{x+2}{3} \right)^{2}-\left( \frac{y-4}{3} \right)^{2}=0\]
move y term to the right hand side. take the square root, solve for y

Answer 6

remember the square root give both a plus and minus, so you end up with 2 different equations, one for each asymptote.

Answer 7

Ok, I think I get it. Thank you.

Answer 8

Wait, so would it be. y +2 = (x-4) and y + 2 = -(x-4)?

Answer 9

So confused >.>

Answer 10

Close, except it's x+2= y-4 and x+2= -(y-4). Of course, the equation of a line is most often put into slope intercept form: y= mx +b. So you should rearrange the equations so y is alone on the left.
See http://www.wolframalpha.com/input/?i=asymptote+x%5E2+-+y%5E2+%2B+4x+%2B+8y+-+21+%3D+0+