The Normal At A Point P on The Ellipse X2 + 4y2 = 16 Meets The x-axis At Q, Then Locus Of M intersects The Latus Rectums Of The Given Ellipse At The Points.

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Question

The normal at a point P on the ellipse x2 + 4y2 = 16 meets the x-axis at Q, then locus of M intersects the latus rectums of the given ellipse at the points.

Solution

Correct option is

Equation of the ellipse is

      

Equation of the normal at  to the ellipse is

      

It meets x-axis at 

If (h, k) are the coordinates of M.

Then 

  

Locus of M is 

Latus rectum of the given ellipse is

          

So locus of M meets the latus rectum at points for which

          

and hence the required points are   

                                                                                                  

 

Testing

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