[SOLVED] Calculus Word Questions

**Soroban** · February 9th 2009, 05:53 AM

Hello, CAIR!

Find the equation of the tangent to the hyperbola: . $\frac{x^2}{16} - \frac{y^2}{9} \:=\:1$
at the point $\left(\text{-}5,\tfrac{9}{4}\right)$ on the curve.

We have: . $9x^2 - 16y^2 \:=\:144$

Differentiate implicitly: . $18x - 32y\frac{dy}{dx} \:=\:0 \quad\Rightarrow\quad \frac{dy}{dx} \:=\:\frac{9x}{16y}$

At $\left(\text{-}5,\tfrac{9}{4}\right),\;\;\frac{dy}{dx} \:=\:\frac{9(\text{-}5)}{16(\frac{9}{4})} \:=\;-\frac{5}{4}$ . . . slope of the tangent

The equation of the line through $\left(\text{-}5,\tfrac{9}{4}\right)$ with slope $m = \text{-}\tfrac{5}{4}$ is:

. . $y - \tfrac{9}{4} \;=\;\text{-}\tfrac{5}{4}(x + 5) \quad\Rightarrow\quad\boxed{ y \:=\:\text{-}\tfrac{5}{4}x - 4}$

**CAIR** · February 9th 2009, 02:07 PM

thanks

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