Question

Find the locus of the points of the intersection of tangents to ellipse  which make an angle θ.

Solution

Correct option is

 

Given ellipse is                                    

            

Equation of any tangent to ellipse (i) in terms of slope (m) is 

          

Since its passes through P(α, β) then 

           

  

   

(ii) being a quadratic equation in m

Let roots of equation (ii) are m1 and m2 then  

  

  

                        

                            

                          

                        

∵ θ be the angle between these two tangents, then  

             

                     

           

    

  

  

      

SIMILAR QUESTIONS

Q1

Find the length of major and minor axes the coordinates of foci and vertices and, the eccentricity of the ellipse 3x2 + 2y2 = 6. Also, find the equation of the directrices.  

Q2

Find the equation of an ellipse whose focus is (–1, 1), eccentricity is  and the directrix is x – y + 3 = 0.

Q3

If the angle between the straight lines joining foci and the ends of the minor axis of the ellipse  is 90o. Find its eccentricity.

Q4

Find the equation of the ellipse referred to its centre whose minor axis is equal to the distance between the foci and whose latus rectum is 10.  

Q5

The extremities of a line segment of length l move in two fixed perpendicular straights lines. Find the locus of that point which divides this line segment in ratio 1 : 2.    

Q6

Find the lengths and equations of the focal radii drawn from the point  on the ellipse 25x2 + 16y2 = 1600.

Q7

 

For what value of λ dose the line y = x + λ touches the ellipse

9x2 + 16y2 = 144.

Q8

Find the equations of the tangents to the ellipse  which are perpendicular to the line y + 2x = 4.

Q9

Find the locus of the foot of the perpendicular drawn from centre upon any tangent to the ellipse .

Q10

Find the locus of the poles of tangents to  with respect to the concentric ellipse .