Question

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

• A. 1/a
• B. –1/a
• C. a
• D. – a

Answer 1

Answer: (B)

–1/a

Answer 2

Given equation of hyperbola xy = a

Slope of tangent at point (x₁ y₁) is

M = $\left( \frac{dy}{dx} \right)_{\left( x_{1},y_{1} \right)}$, ∴ $\frac{xdy}{dx}$+ y = 0 ⇒ $\frac{dy}{dx} - \frac{- y}{x}$

At point (a, 1); m = $\left( \frac{dy}{dx} \right)_{(a,1)}$ = - $\frac{1}{a}$.