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  • 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 poi

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

Option: 1

\mathrm{\frac{13}{8}}


Option: 2

\mathrm{\frac{7}{4}


Option: 3

\mathrm{\frac{15}{8}}


Option: 4

2


Answers (1)

best_answer

Slope of tangent at  \mathrm{\left(2, \frac{1}{2}\right)}

\mathrm{\begin{aligned} & m=-\frac{1}{4} \\ & \tan \theta=\frac{1}{4} \\ & \theta=\phi-90^{\circ} \\ & \tan \theta=4 \\ & \text { Slope of incident ray }=m \\ & \left|\frac{m-\left(-\frac{1}{4}\right)}{\mid}\right|=\tan \theta=4 \\ & \left|\frac{4 m+1}{4-m}\right|=4 \\ & 4 m+1=16-4 m \\ & m=\frac{15}{8} \end{aligned}}

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Rishi

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