KVPY SX SB Exam 2015 Question Paper

Question : 83 of 120

Marks: +1, -0

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 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 -

Solution:

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}|=|{4 -∞}/{1+ 4.∞}|

{4 -m}/{1+ 4m}=±1/4

m=15/8

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