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Question

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
3x5y+25=0
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B
3x+5y+25=0
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C
3x+5y=25
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D
3x5y=25
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Solution

The correct options are
B 3x+5y+25=0
D 3x5y=25

Here a2=25
and
b2=16
e=11625=35

Let point Q be (h,k), where k<0
Given that k=SP=a±ex1, where P(x1,y1) lies on the ellipse

|k|=a±eh (as x1=h)
y=a±ex
3x+5y+25=0 or 3x5y=25

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