## Question

For what value of *c* does not line *y* = 2*x* + *c* touches the hyperbola 16*x*^{2} – 9*y*^{2} = 144?

### Solution

**20**

Equation of hyperbola is

16*x*^{2} – 9*y*^{2} = 144

Comparing this with , we get *a*^{2} = 9, *b*^{2} = 16.

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

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

16*x*^{2} – 9*y*^{2} = 144 then *c*^{2} = *a*^{2}*m*^{2} – *b*^{2}

⇒ c^{2} = 9(2)^{2} – 16 = 36 – 16 = 20

#### SIMILAR QUESTIONS

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