Question

If the tangents are drawn to the ellipse x2 + 2y2 = 2, then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is

Solution

Correct option is

 

We have, 

          

The equation of any tangent to this ellipse in parametric form at point  is   

     

This cuts the coordinate axes at points. Let P(hk) be the mid-point of intercept AB. Then, 

            

  

    

   

Hence, the locus of (hk) is  

      .

SIMILAR QUESTIONS

Q1

The locus of the point of intersection of tangents to the ellipse  at the points whose eccentric angles differ by  is  

Q2

The locus of the point of intersection of tangents to the ellipse , which make complementary angles with x-axis, is 

Q3

The locus of the foot of the perpendicular drawn from the centre of the ellipse  on any tangent is 

Q4

, be the end points of the latusrectum of the ellipse x2 + 4y2 = 4. The equations of parabolas with latusrectum PQ are 

Q5

The locus of the point of intersection of perpendicular tangents to.

Q6

S(3, 4) and S’(9, 12) are two foci of an ellipse. If the foot of the perpendicular from S on a tangent to the ellipse has the coordinates (1, –4), then the eccentricity of the ellipse is  

Q7

The tangent at a point P(θ) to the ellipse  cuts the auxiliary circle at points Q and R. If QR subtends a right angle at the centre C of the ellipse, then the eccentricity of the ellipse is

Q8

Let d1 and d2 be the lengths of the perpendiculars drawn from fociS and S’ of the ellipse  to the tangent at any point P on the ellipse. Then, SP : SP’ = 

Q9

The eccentricity of an ellipse with centre at the origin and axes along the coordinate axes, is 1/2. If one of the directrices is x = 4, then the equation of the ellipse is  

Q10

If A bar of given length moves with its extremities on two fixed straight lines at right angles, then the locus of any point on the bar describes a/an