A mirror in the first quadrant is in the shape of a hyperbola whose equation is xy=1. A light source in the second quadrant emits a beam of light that the hits the mirror at the point (2,1/2). If the reflected ray is parallel to the y-axis , the slope of the incident beam is

Options

A. `(13)/(8)`
B. `(1)/(4)`
C. `(15)/(8)`
D. 2

Answer

C

Explanation

Curve `y=(1)/(x)`
`(dy)/(dx)=-(1)/(x^(2))`
slope of tangent `=-(1)/(4)at (2,(1)/(2))`
slope of normal =4
where foot of normal is `= (2,(1)/(2))`
let slope at incident beam is 'm'
`|(4-m)/(1+4m)|=|(oo-4)/(1-4.oo)|`
`(4-m)/(1+4m)=+-(1)/(4)`
`m=(15)/(8)`