For What Value Of λ Dose The Line y = x + λ Touches The Ellipse 9x2 + 16y2 = 144.

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Question

 

For what value of λ dose the line y = x + λ touches the ellipse

9x2 + 16y2 = 144.

Solution

Correct option is

 

∵ Equation of ellipse is

         

  

Comparing this with  

       

then we get 

    a2 = 16 and b2 = 9 

and comparing the line y = x + λ with y = mx + c

  

If the line y = x + λ touches the ellipse    

       

then,   

       

  

.

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