What is the slope of the tangent line drawn t | vedclass

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Question

(b) Given equation of hyperbola $xy = a$

Slope of tangent at point $({x_1}\,{y_1})$ is

$m = {\left( {\frac{{dy}}{{dx}}} \right)_{({x_1},\,{y_1})

Vedclass · Accepted Answer

$-1/a$

Vedclass · Answer

(b) Given equation of hyperbola $xy = a$

Slope of tangent at point $({x_1}\,{y_1})$ is

$m = {\left( {\frac{{dy}}{{dx}}} ight)_{({x_1},\,{y_1})}}$

$	herefore \,\frac{{xdy}}{{dx}} + y = 0$

==> $\frac{{dy}}{{dx}} = \frac{{ - y}}{x}$

At point $(a,\,1);$ $m = {\left( {\frac{{dy}}{{dx}}} ight)_{(a,\,1)}} = - \frac{1}{a}$.

What is the slope of the tangent line drawn to the hyperbola $xy = a\,(a \ne 0)$ at the point $(a, 1)$

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