Question

 

The value of λ for which the line y = x + λ  touches the ellipse

9x2 + 16y2 = 144, are

Solution

Correct option is

±5

 

The equation of the line is  

      

Comparing it with y = mx + c, we get  

      m = 1 and c = λ  

The equation of the ellipse is    

          

  

Comparing the with , we get a2 = 16 and b2 = 9. 

If the line touches the ellipse, then  

       

  

.

SIMILAR QUESTIONS

Q1

 

The foci of the ellipse  are  

 

Q2

The vertices of the ellipse 

Q3

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

Q4

 

For the ellipse

       

lengths of major and minor axes are respectively.

Q5

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

Q6

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

Q7

If the line lx + my + n = 0 cuts the ellipse  in points whose eccentric angles differ by π/2, then

Q8

If the line lx + my + n = 0 to touches the ellipse , then

Q9

 

The line  is a tangent to the ellipse

 .