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KVPY2015MathematicsHyperbola

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

Options

  1. A13 8
  2. B7 4
  3. C15 8
  4. D2

Correct answer

C. 15 8

Step-by-step solution

Slope of tangent at (2, 1 2 ) array l m =- 1 4 =- 1 y = -90^ =4 array Slope of incident ray = m array l | m- (- 1 4 ) 1+m (- 1 4 ) |= =4 | 4 m+1 4-m |=4 4 m+1=16-4 m m= 15 8 array

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