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)

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