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

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Question

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

Solution

Correct option is

 

The centre of the ellipse is at the mid-point of its foci. So, coordinates of centre are (2, 1). 

Clearly, two foci lie on the line x = 2. So, major axis is parallel to y-axis. 

The distance between two foci is 6.   

.  

Now,  

     

   

Hence, the equation of the ellipse is  

      

Testing

SIMILAR QUESTIONS

Q1

 

The curve represented by the equation

 , is

Q2

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

Q3

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

Q4

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

Q5

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

Q6

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

Q7

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

Q8

 

The foci of the ellipse  are  

 

Q9

The vertices of the ellipse 

Q10

 

For the ellipse

       

lengths of major and minor axes are respectively.