Question

The equation of tangent to the hyperbola
$xy=16$ at the point $\text{P}\left(2\right)$ in the first quadrant is:

• A. $2x+y=16$
• B. $x+4y=16$
• C. $x+2y=16$
• D. $2x+y=8$

Answer 1

The correct option is B $x+4y=16$

Given, $xy=16,$
$\text{P}\left(2\right)\Rightarrow t=2$
$\Rightarrow c^2=16\Rightarrow c=\pm 4$
As it lies in first quadrant.
So, we take
$\Rightarrow c=4$
Equation of tangent on hyperbola
$xy=c^2\text{at the point}P\left(t\right)\text{is}$
$x+y{t}^2=2ct$
Putting the values of $t$ we get
$\Rightarrow x+y\times 2^2=2\times 4\times 2$
$\Rightarrow x+4y=16$
Hence, the correct answer is Option (b).