From any point P lying in the first quadrant on the ellipse x225+y216=1,PN is drawn perpendicular to the major axis and produced at Q so that NQ equals to PS′, where S′ can be any foci. Then the locus of Q can be
A
3x−5y+25=0
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B
3x+5y+25=0
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C
3x+5y=25
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D
3x−5y=25
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Solution
The correct options are B3x+5y+25=0 D3x−5y=25
Here a2=25 and b2=16 ⇒e=√1−1625=35
Let point Q be (h,k), where k<0 Given that k=S′P=a±ex1, where P(x1,y1) lies on the ellipse
⇒|k|=a±eh(as x1=h) ⇒−y=a±ex ⇒3x+5y+25=0 or 3x−5y=25