question_answer

The line \[\frac{x}{a}-\frac{y}{b}=1\] cuts the \[x-\]axis at \[P\]. The equation of the line through \[P\] perpendicular to the given line is:

A) \[x+y=ab\]                         

B) \[x+y=a+b\]

C) \[ax+by={{a}^{2}}\]                       

D)  \[bx+ay={{b}^{2}}\]

Correct Answer: C

Solution :

Given equation of a line is Its slope is\[\frac{b}{a}\]. \[\therefore \]The equation of line passing through a point \[P(a,\,\,0)\] and perpendicular to the given line whose slope is\[-\frac{a}{b},\,\,\text{is}\]                 \[y-0=-\frac{a}{b}(x-a)\]            \[by+ax={{a}^{2}}\]