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Question

A ray eminating from the point (3,0) is incident on the ellipse 16x2+25y2=400 at the point P with ordinate 4. Equation of the reflected ray is

A
4x+3y+12=0
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B
4x+3y=12
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C
3x+4y=16
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D
3x+4y+9=0
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Solution

The correct option is B 4x+3y=12
Given ellipse :16x2+25y2=400
16x2+25(4)2=400

The co-ordinate of P=(0,4)

Foci are (±ae,0)=(±3,0)
ray is eminating from one of the focus hence after reflection it will pass through other focus i.e. (3,0)
Therefore, the equation of the reflected ray will be x3+y4=1 or 4x+3y=12

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