# 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.