Question

Find the equation of the ellipse referred to its centre whose minor axis is equal to the distance between the foci and whose latus rectum is 10.  

Solution

Correct option is

 

Let the equation of the ellipse is   

                          

Then the foci are S(ae, 0) and S’(–ae, 0) length of minor axisBB’ = 2b and length of latus rectum 

∴ According to the question                  

          BB’ = SS’   

    

  

and,  

  

also we have 

        

Putting the value of b from equation (i) in equation (ii), we have   

       

  

From equation (i), we have 

       

  

    

From equation (ii), 

      

Putting the values of a and b in , the equation of required ellipse is  

      

      .

SIMILAR QUESTIONS

Q1

To find the equation of an ellipse from the definition that ellipse is the locus of a point which moves such that the sum of its distances from two fixed points is constant with the fixed points as foci.

Q2

Find the length of major and minor axes the coordinates of foci and vertices and, the eccentricity of the ellipse 3x2 + 2y2 = 6. Also, find the equation of the directrices.  

Q3

Find the equation of an ellipse whose focus is (–1, 1), eccentricity is  and the directrix is x – y + 3 = 0.

Q4

If the angle between the straight lines joining foci and the ends of the minor axis of the ellipse  is 90o. Find its eccentricity.

Q5

The extremities of a line segment of length l move in two fixed perpendicular straights lines. Find the locus of that point which divides this line segment in ratio 1 : 2.    

Q6

Find the lengths and equations of the focal radii drawn from the point  on the ellipse 25x2 + 16y2 = 1600.

Q7

 

For what value of λ dose the line y = x + λ touches the ellipse

9x2 + 16y2 = 144.

Q8

Find the equations of the tangents to the ellipse  which are perpendicular to the line y + 2x = 4.

Q9

Find the locus of the foot of the perpendicular drawn from centre upon any tangent to the ellipse .

Q10

Find the locus of the points of the intersection of tangents to ellipse  which make an angle θ.