Rational Functions Question

1. Nov 23, 2007

Sorry!

1. The problem statement, all variables and given/known data
Find two constants for 'a' and 'b' such that the verticle asymptote will be $$\pm$$ $$\frac{3}{5}$$

y=$$\frac{ax^2+7}{9-bx^2}$$

I rearranged so that it becomes $$-bx^2+8$$ in the denominator since i know that there are two roots that are $$\pm$$ it must be a square and since 3 is the numerator of the root it must -9 .... so i rearranged again to get

y=$$\frac{-ax^2-7}{bx^2-9}$$

in which case i found the constant for a (-1) and $$5^2$$ is 25 so i found b as well so the equation would be

y=$$\frac{-x^2-7}{25x^2-9}$$

is this right??? I have no way to check my answer so i just want to make sure :D

2. Nov 23, 2007

rock.freak667

well for a vertical asymptote...the denominator of the function should be zero
in your case $9-bx^2=0$
so that $x=\pm\fract{3}{\sqrt{b}}$
so then equate that to $\pm\frac{3}{5}[/tex] and find b 3. Nov 23, 2007 Sorry! not gonna lie i don't get it... would 25x^2-9 give u two values of x that equate to 0??? (5x-3)(5x+3). I just don't understand what your doing there lol. 4. Nov 23, 2007 symbolipoint Another try: you want [itex]9-bx^2=0$
when x = +3/5 and x = -3/5; so if you want to do this in a crude way, just find the expression for b. This is b=(-9)/(x^2). So what is x ? You were already given the x values, since you want the vertical asymtotes at x=+3/5 and x=-3/5. Find b for both of these values by substituting. ...
b=25.

I see no particular big restrictions on a, except that a is not equal to zero.

5. Nov 23, 2007

rock.freak667

Can't it be for all values of a? as the value of 'a' doesn't affect the vertical asymptotes

6. Nov 23, 2007

Sorry!

yah all values can be 'a'. i just made it -1 so that the denominator would have better form.... i think i did that right i wasn't EXACTLY sure if i could change all the signs in the equation by multiplying thru by -1 to move the negative to the top ??? :S

7. Nov 24, 2007

Dick

The value of 'a' can affect the asymptotes if it happens to be -7*5^2/3^3.

8. Nov 24, 2007

Sorry!

the 'a' value affects horizontal asymptote if the powers are the same. The only factor for the vertical asymptotes is that it makes the denominator 0 without making the numerator 0.