Question

If the line $y=2x+k$ be a tangent to the hyperbola $36x^2-25y^2=3600$, then $k=$

• A. $16$
• B. $-16$
• C. $\pm 16$
• D. None of these

Answer 1

The correct option is A $16$

We have given that

$y=2x+k$ -----(i)

$\frac{dy}{dx}=2$

And,

$36x^2-25y^2=3600$

Now,

$72x-50y\frac{dy}{dx}=0$

$\Rightarrow 72x-50y\times 2=0$

$\Rightarrow 72x-100y=0$ -------(ii)

From (i) and (ii) we have,

$k=16$

Hence, the option $\left(A\right)$ is correct answer.