A ray emitting from the point (−3,0) is incident on the ellipse 16x2+25y2=400 at point P with an ordinate 4. If the equation of the reflected ray after first reflection is 4x+3y=k, then the value of k is
A
12
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B
−12
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C
9
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D
−9
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Solution
The correct option is A12 16x2+25y2=400⇒x225+y216=1 a=5,b=4 ∴c=√25−16=3
Coordinates of foci are (±c,0)
i.e., S(3,0) and S′(−3,0)
We know that, ray emitting from focus S′ after striking the ellipse at P, will pass through other focus S.
Hence, point S(3,0) lies on the given line 4x+3y=k. ⇒4(3)+0=k⇒k=12