If the points (a,0), (0,b) and (3,2) are collinear, then find 2b+3a.

# If the points (a,0), (0,b) and (3,2) are collinear, then find $\frac{2}{b}+\frac{3}{a}$.

1. A
0
2. B
1
3. C
2
4. D
3

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### Solution:

Given that the points (a,0), (0,b) and (3,2) are collinear.
Area of the triangle formed is 0.
$⇒\frac{1}{2}\left[a\left(b-2\right)+0\left(2-0\right)+3\left(0-b\right)\right]=0$
$⇒\mathit{ab}-2a-3b=0$
$⇒2a+3b=\mathit{ab}$
$⇒\frac{2}{b}+\frac{3}{a}=1$

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