Question

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  

Solution

Correct option is

 

Let the equation of the ellipse be 

We have, 

          

  

  

  

Hence, the equation of the ellipse is

               

SIMILAR QUESTIONS

Q1

The locus of the foot of the perpendicular from the foci on any tangent to the ellipse 

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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  

Q8

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

Q9

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’ = 

Q10

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