If SY and S1Y1 be Perpendiculars From The Foci Upon The Tangent AtP of An Ellipse, Then Y and Y1 lie On The Auxiliary Circle AndSY.S1Y1 =    

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Question

If SY and S1Y1 be perpendiculars from the foci upon the tangent atP of an ellipse, then Y and Y1 lie on the auxiliary circle andSY.S1Y1 =    

Solution

Correct option is

b2

 

Equation of tangent at is 

          

 

Equation of the perpendicular to (i) and passing through (ae, 0) is

      

For locus of Y, eliminate Ï• from equations (i) and (ii), for which squaring and adding (i) and (ii), we get 

      

                                                       

   

Hence locus of Y is the auxiliary circle. Similarly, as above we can prove that the locus of point Y1 is the auxiliary circle. 

                                     

                                 

                                 

                                  = b2.     

SIMILAR QUESTIONS

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Q8

 

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Q9

 

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Q10

Find the condition on a and b for which two distinct chords of the ellipse  passing through (a, –b) are bisected by the line x + y = b