Question

If the three points $(3q, 0), (0, 3p)$ and $(1, 1)$ are collinear then which one is true ?

• A. $\frac{1}{p}+\frac{1}{q} = 1$
• B. $\frac{3}{p}+\frac{1}{q} = 1$
• C. $\frac{1}{p}+\frac{1}{q} = 3$
• D. $\frac{1}{p}+\frac{3}{q} = 1$

Answer 1

Answer: (C)

$A(3 q, 0), B(0,3 p), C(1,1)$
are collinear.
$\therefore $ slope of $A C=$ slope of $B C$
$\Rightarrow \frac{1-0}{1-3 q}=\frac{1-3 p}{1-0} $
$ \Rightarrow \frac{1}{1-3 q}=\frac{1-3 p}{1}$
$\Rightarrow 1=(1-3 p)(1-3 q) $
$ \Rightarrow 1=1-3 q-3 p+9 p q$
$\Rightarrow 3 p+3 q=9 p q$
$\frac{1}{q}+\frac{1}{p}=3$