Question

Find the equation of line passing through (2, 3) and perpendicular to the line 3x + 4 y - 5 = 0.

Answer 1

We have, equation of line is 3x + 4y - 5 = 0

The equation of line perpendicular to the given line is $4x-3y=\lambda$

This line passes through (2, 3).

Put x = 2 and y = 3 in Eq. (i), we get

4(2) - 3(3) = $\lambda \Rightarrow 8-9=\lambda \Rightarrow \lambda =-1$

On putting the value of $\lambda$ in Eq. (i), we get 4x - 3y = -1

So, the equation of line is 4x - 3y + 1 = 0