The Equation Of The Ellipse Whose Axes Are Of Lengths 6 And  and Their Equations Are x – 3y + 3 = 0 And 3x + y – 1 = 0 Respectively, Is

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Question

The equation of the ellipse whose axes are of lengths 6 and  and their equations are x – 3y + 3 = 0 and 3x + y – 1 = 0 respectively, is

Solution

Correct option is

 

Let P(xy) be nay point on the ellipse and let p1 and p2 be the lengths of the perpendiculars draw from P on the major and minor axes of the ellipse. Then,  

         

Let 2a and 2b be the lengths of the major and minor axes of the ellipse,  

We have, 

           

.  

The equation of the ellipse is  

       

   

  

Testing

SIMILAR QUESTIONS

Q1

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

Q2

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

Q3

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

Q4

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

Q5

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

Q6

 

The foci of the ellipse  are  

 

Q7

The vertices of the ellipse 

Q8

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

Q9

 

For the ellipse

       

lengths of major and minor axes are respectively.

Q10

The eccentric angle of the extremities of latusrecta of the ellipse  are given by