Question

The equation of the tangent to the curve $x=\sqrt{t},y=t-\frac{1}{\sqrt{t}}$ at $t=4$ is:

• A. $x-4y=20$
• B. $17x-4y=20$
• C. $17x+4y=20$
• D. $4x-17y=20$

Answer 1

The correct option is B $17x-4y=20$

Given, $x=\sqrt{t}$.......(1), $y=t-\frac{1}{\sqrt{t}}$........(2).

When $t=4$,$x=2,y=4-\frac{1}{2}=\frac{7}{2}$.

Using $\left(1\right)$ in $\left(2\right)$ we get,

$y=x^2-\frac{1}{x}$.

$\Rightarrow \frac{dy}{dx}=2x+\frac{1}{x^2}$

$\Rightarrow \frac{dy}{dx}{|}_{x=2}=\frac{17}{4}$.

Now, equation of tangent at $(2,\frac{7}{2})$ is

$y-\frac{7}{2}=\frac{17}{4}(x-2)$

or, $17x-4y=20$.