Question

The equation of the ellipse whose axes are along the coordinate axes, vertices are (0, ±10) and eccentricity e = 4/5, is 

Solution

Correct option is

 

Let the equation of the required ellipse be  

           

Since the vertices of the ellipse are on y-axis. So, the coordinates of the vertices are (0, ±b). 

∴   b = 10 

The eccentricity is given by   

      

Substituting the values of a2 and b2 in (i), we obtain  

      

as the equation of the required ellipse.

SIMILAR QUESTIONS

Q1

The equation  represents an ellipse, if  

Q2

The curve with parametric equations 

Q3

 

The curve represented by

 

Q4

Length of the major axis of the ellipse , is

Q5

The length of the axes of the conic 9x2 + 4y2 – 6x + 4y + 1 = 0 are

Q6

The eccentricity of the ellipse 

Q7

 

If the eccentricities of the two ellipse 

are equal, then the value , is

Q8

 

The curve represented by the equation

 , is

Q9

The equation of the ellipse whose axes are along the coordinate axes, vertices are (±5, 0) are foci at (±4, 0), is 

Q10

If the latusrectum of an ellipse is equal to one half of its minor axis, then the eccentricity is equal to