Question

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

Solution

Correct option is

 

The given conic can be re-written as 

      

Shifting the origin at (3, 0) without rotating the coordinates axes,

We have, 

        

The equation of the ellipse with reference to new axes is  

      

Comparing this equation with the standard equation  

      .     

Let e be the eccentricity of the given conic. Then, 

      

         

         

The coordinates of foci with respect to new origin are  

        

Substituting these in (i), we obtain (3, ±3) as the coordinates of foci.

SIMILAR QUESTIONS

Q1

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

Q2

The eccentricity of the ellipse 

Q3

 

If the eccentricities of the two ellipse 

are equal, then the value , is

Q4

 

The curve represented by the equation

 , is

Q5

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

Q6

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

Q7

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

Q8

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

Q9

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

Q10

 

The foci of the ellipse  are