Question

The slope of tangent to the hyperbola
$xy=2a^2\text{at the point}(a,2a)\text{is}$

Answer 1

Given,
$xy=2a^2,$
$\text{Equation of tangent on hyperbola}$
$xy=c^2\text{at the point}P(x_1,y_1)\text{is}$
$\Rightarrow x{y}_1+y{x}_1=2c^2$
$\text{Point}:(x_1,y_1)\equiv (a,2a)$
$\text{Slope of the line}=-\frac{y_1}{x_1}\text{Slope of the line}=-\frac{2a}{a}\text{Slope of the line}=-2$