A ray of light is sent along the line which passes through the point (2, 3). The ray is reflected from the point P on x-axis. If the reflected ray passes through the point (6, 4), then the coordinates of P are

Let P≡α,0. Let the reflected ray makes an angle θ with +ve direction of x-axis, then the incident ray makes angle π-θ with positive direction of x-axis. The slope of the incident ray is=0-3α-2=tanπ-θ i.e., tanθ=3α-2The slope of the reflected ray is=4-06-α=tanθ i.e., tanθ=46-αFrom Eq. (1) and (2), we get3α-2=46-α⇒18-3α=4α-8⇒7α=26  or  α=267∴The coordiantes of A are 267,0