Question

If the line lx + my + n = 0 cuts the ellipse  in points whose eccentric angles differ by π/2, then

Solution

Correct option is

 

Suppose the line lx + my + n = 0 cuts the ellipse at . Then, these two points lie on the given line.

  

and, 

     

and,

     

.

SIMILAR QUESTIONS

Q1

The eccentricity of the ellipse, if the distance between the foci is equal to the length of the latusrectum, is 

Q2

The equation of the circle drawn with the two foci of  as the end-points of  a diameter, is

Q3

The foci of the conic 25x2 +16y2 – 150x = 175 are

Q4

 

The foci of the ellipse  are  

 

Q5

The vertices of the ellipse 

Q6

The equation of the ellipse, with axes parallel to the coordinate axes, whose eccentricity is 1/3 and foci are at (2, –2) and (2, 4) is

Q7

 

For the ellipse

       

lengths of major and minor axes are respectively.

Q8

The equation of the ellipse whose axes are of lengths 6 and  and their equations are x – 3y + 3 = 0 and 3x + y – 1 = 0 respectively, is

Q9

The eccentric angle of the extremities of latusrecta of the ellipse  are given by

Q10

If the line lx + my + n = 0 to touches the ellipse , then