The Value Of λ For Which The Line y = x + λ  touches The Ellipse 9x2 + 16y2 = 144, Are

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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  

       

  

.

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