The line `x/a-y/b=1` cuts the x-axis at P. The equation of the line through P and perpendicular to the given line is

Options

A. `x+y=ab`
B. `x+y=a+b`
C. `ax+by=a^(2)`
D. `bx+ay=b^(2)`

Answer

C

Explanation

The line `(x)/(a)-(y)/(b)=1` cuts x-axis at P(a,0). The equation of the line through P(a,0) and perpendicular to `(x)/(a)-(y)/(b)=1`, is
`y-0=-(a)/(b)(x-a) implies ax+by=a^(2)`