Question

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

Solution

Correct option is

 

Let the equation of the required ellipse be 

         

The coordinates of its vertices and foci are (±a, 0) and (±ae, 0) respectively. 

     

Now, 

      

           = 9. 

Substituting the values of a2 and b2 in (i), we get , which is the equation of the required ellipse.

SIMILAR QUESTIONS

Q1

The normal at a point P on the ellipse x2 + 4y2 = 16 meets the x-axis at Q. If M is the mid-point of the line segment PQ then the locus of M intersects the latusrectums of the given ellipse at the points    

Q2

The equation  represents an ellipse, if  

Q3

The curve with parametric equations 

Q4

 

The curve represented by

 

Q5

Length of the major axis of the ellipse , is

Q6

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

Q7

The eccentricity of the ellipse 

Q8

 

If the eccentricities of the two ellipse 

are equal, then the value , is

Q9

 

The curve represented by the equation

 , is

Q10

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