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

Line perpendicular to the given line `(x)/(a)-(y)/(b)=1`
`(x)/(b)+(y)/(a)+lambda=0`
According to the question, line (i) is passing through the point P(a, 0)
`(a)/(b)+0+lambda=0`
`lambda=(-a)/(b)`
Put the value of `lambda` in equation (i), we get `(x)/(b)+(y)/(a)-(a)/(b)=0`
`ax+by=a^(2)`