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  • A ray emanating from the point  is incident on the ellipse

A ray emanating from the point \left ( -0,3 \right ) is incident on the ellipse \mathrm{16 x^2+25 y^2=400} at the point P with ordinate 4. Then the equation of the reflected ray after first reflection is.   

Option: 1

\mathrm{4 x+3 y=12}


Option: 2

\mathrm{3 x+4 y=12}


Option: 3

\mathrm{4 x-3 y=12}


Option: 4

\mathrm{3 x-4 y=12}


Answers (1)

best_answer

(a) For point P y-coordinate =4

Given ellipse is \mathrm{16 x^2+25 y^2=400}
\mathrm{16 x^2+25(4)^2=400, \therefore x=0}
co-ordinate ofco-ordinate of \mathrm{P \text { is }(0,4)}
\mathrm{e^2=1-\frac{16}{25}=\frac{9}{25}}                                          
\mathrm{\quad e=\frac{3}{5}}
\mathrm{\therefore \text { Foci }( \pm a e, 0) \text {, i.e. }( \pm 3,0)}
Equation of reflected ray 
\mathrm{\left(\text { i.e.PS) is } \frac{x}{3}+\frac{y}{4}=1 \text { or } 4 x+3 y=12\right. \text {. }}

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