Question

The equation of normal to the hyperbola $xy=25$ at the point $\text{P}\left(2\right)$ in the first quadrant is

• A. $8x+2y-75=0$
• B. $8x+2y+75=0$
• C. $8x-2y-75=0$
• D. $8x-2y+75=0$

Answer 1

The correct option is C $8x-2y-75=0$

Given, $xy=25$
$\text{P}\left(2\right)\Rightarrow t=2$
$\Rightarrow c^2=25\Rightarrow c=5$
as it lies in first quadrant
Equation of normal to the hyperbola $xy=c^2$ at the point P$\left(t\right)$ is $x{t}^3-yt-c{t}^4+c=0$
Put the values of $t\text{and}c$
$\Rightarrow x(2{)}^3-y(2)-c(2{)}^4+5=0$
$\Rightarrow 8x-2y-16\times 5+5=0$
$\Rightarrow 8x-2y-75=0$
Hence, the correct answer is Option a.