For What Value Of c does Not Line y = 2x + c touches The Hyperbola 16x2 – 9y2 = 144?

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For what value of c does not line y = 2x + c touches the hyperbola 16x2 – 9y2 = 144?


Correct option is


Equation of hyperbola is

        16x2 – 9y2 = 144          

 Comparing this with , we get a2 = 9, b2 = 16.

And comparing this line y = 2x + c with y = mx + c. ⇒m = 2, c = 1

If the line y = 2x + 1 touches the hyperbola

              16x2 – 9y2 = 144    then    c2 = a2m2 – b2

⇒ c2 = 9(2)2 – 16 = 36 – 16 = 20                 



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