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Q.

If tanθ1tan θ2=-a2b2 then the chord joining two points θ1 and θ2 on the ellipse x2a2+y2b2=1 will subtend a right angle at

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a

centre 
 

b

end of major axis 
 

c

end of minor axis 
 

d

focus

answer is B.

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Detailed Solution

 

Let end points  of chord be P(a cosθ1, b sinθ1) and  Q(acosθ2, bsinθ2) centre C(0, 0) Now slope of CP=b sinθ1a cosθ1 m1=ba Tanθ1                  slope of CQ=b sinθ2a cosθ2                 m2=ba Tanθ2 Now m1m2=ba Tanθ1ba Tanθ2 m1m2=b2a2Tanθ1Tanθ2                  =b2a2(-a2b2)                  =-1            chord makes right angle at centre

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