Finding Constants for Rational Functions with Specific Vertical Asymptotes

[Sorry!]

Homework Statement

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

 

[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 [itex]\pm\frac{3}{5}[/tex] and find b

 

[Sorry!]

not going to 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.

 

[symbolipoint]

Another try: you want $9-bx^2=0$
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.

 

[rock.freak667]

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

 

[Sorry!]

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

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

 

[Dick]

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

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

 

[Sorry!]

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

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.