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