# Asymptote of curves problems

1. Aug 17, 2010

### thereddevils

1. The problem statement, all variables and given/known data

Find the set of values of m such that the asymtote of the curve,
$$y=\frac{3(m+1)x+m-2}{(m-2)x+3m}$$ intersect at a point above the line y=3x-2

2. Relevant equations

3. The attempt at a solution

Vertical asymtote, x=-3m/(m-2)

horizontal asymtote, y=3(m+1)/(m-2)

i am not sure how to move on.

2. Aug 17, 2010

### Staff: Mentor

Re: asymtotes

I believe this should say "such that the asymptotes of the curve..."
The vertical and horizontal asymptotes intersect at (-3m/(m - 2), 3(m + 1)/(m - 2)). For this point to be above the corresponding point on the line y = 3x - 2, what are the conditions on m?

3. Aug 17, 2010

### thereddevils

Re: asymtotes

I think all the intersections must lie on the line y=3x-1 but i am not sure what kind of conditinos to be imposed on m.

4. Aug 17, 2010

### Staff: Mentor

Re: asymtotes

No, it asks you to find the set of values of m such that the asymptotes of the curve...
intersect at a point above the line y=3x-2.

The two asymptotes intersect at (-3m/(m - 2), 3(m + 1)/(m - 2)). What are the coordinates of the line y = 3x - 2 when x = -3m/(m - 2)?

What are the conditions on m so that the asymptote intersection is above the point on the line at which x = -3m/(m - 2)?

5. Aug 18, 2010

### thereddevils

Re: asymtotes

ok, i will find y when x=-3m/(m-2)

After this, do i calculate y>-3m/(m-2) for the ranges of m?

6. Aug 18, 2010

### Staff: Mentor

Re: asymtotes

Set up the inequality with the y value at the point of intersection (of the asymptotes) on one side, and the y value of the line on the other. For both points, use the same x value.

7. Aug 18, 2010

### thereddevils

Re: asymtotes

ok thanks Mark.

8. Aug 22, 2010

### thereddevils

Re: asymtotes

Is the answer m<14/52 and m>2 ?