# Coordinate geometry--

• Oct 19th 2010, 08:52 AM
Ilsa
Coordinate geometry--
Find the equation of the line through the point (5,2) and parallel to the line 2y-3x=4. Find the value of a if the line ax-(a+1)y+2=0 does not intersect the pair of parallel lines.

The underlined part is what i could not get.
• Oct 19th 2010, 08:01 PM
bigwave
rewrite
Quote:

Originally Posted by Ilsa
Find the equation of the line through the point (5,2) and parallel to the line 2y-3x=4. Find the value of a if the line ax-(a+1)y+2=0 does not intersect the pair of parallel lines.

The underlined part is what i could not get.

well this is a try at it...rewrite
$\displaystyle 2y-3x=4$ as $\displaystyle y=\frac{3}{2}x+2$
Then at $\displaystyle (5,2)$ the eq is $\displaystyle y=\frac{3}{2}x-\frac{11}{2}$
• Oct 19th 2010, 10:57 PM
earboth
correction
Quote:

Originally Posted by Ilsa
Find the equation of the line through the point (5,2) and parallel to the line 2y-3x=4. Find the value of a if the line ax-(a+1)y+2=0 does not intersect the pair of parallel lines.

The underlined part is what i could not get.

1. The pair of parallel lines have the common slope $\displaystyle m = \frac32$.

2. $\displaystyle ax-(a+1)y+2=0~\implies~y=\dfrac{a}{a+1} \cdot x + \dfrac2{a+1}$

3. If the line in question doesn't intersect the two parallels it must be parallel to both, that means it's slope must be $\displaystyle m = \frac32$ too. Therefore:

$\displaystyle \dfrac{a}{a+1}=\dfrac32~\implies~2a=3a+3~\implies~ a=-3$

Hence $\displaystyle a=-3$