Coordinate Geometry Question 10
Question: If the points $ (a,0),\ (0,b) $ and (1, 1) are collinear, then
Options:
A) $ \frac{1}{a^{2}}+\frac{1}{b^{2}}=1 $
B) $ \frac{1}{a^{2}}-\frac{1}{b^{2}}=1 $
C) $ \frac{1}{a}+\frac{1}{b}=1 $
D) $ \frac{1}{a}-\frac{1}{b}=1 $
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Answer:
Correct Answer: C
Solution:
$ \frac{1}{2} \begin{vmatrix} a & 0 & 1 \\ 0 & b & 1 \\ 1 & 1 & 1 \\ \end{vmatrix} |=0\Rightarrow a(b-1)+0+1(-b)=0 $
$ \Rightarrow ab-a-b=0\Rightarrow \frac{1}{a}+\frac{1}{b}=1 $ .
BETA
