Question

The equation of tangent drawn to the curve $xy=4$ from point $(0,1)$ is

• A. $y-\frac{1}{2}=-\frac{1}{16}(x+8)$
• B. $y-\frac{1}{2}=-\frac{1}{16}(x-8)$
• C. $y+\frac{1}{2}=-\frac{1}{16}(x-8)$
• D. $y-8=-\frac{1}{16}$

Answer 1

The correct option is A $y-\frac{1}{2}=-\frac{1}{16}(x+8)$

$xy=4$ at pojnt $(0,1)$

Equation of tangent is given by $(y-y_1)=M(x-x_1)$

$M=\frac{dy}{dx}$ of the curve

$xy=4$

$\Rightarrow y=4/x$

$\frac{dy}{dx}=\frac{-4}{x^2}$

$M=\frac{-4}{0}=\infty$

$(y-y_1)=M(x-x_1)$

$(y-1)=\infty (x-0)$

$y-1=\infty$.