# Use implicit differentiation to find an equation of the tangent line to the curve at the given...

## Question:

Use implicit differentiation to find an equation of the tangent line to the curve at the given point.

{eq}x^{2}-xy-y^{2}=1,(2,1) {/eq} hyperbola

## Equation of Tanget Line:

Given an implicit function {eq}f(x,y)=0 {/eq}, the equation of the tangent line at a point {eq}(x_0,y_0) {/eq} is equal to

{eq}y(x) = f(x_0) + f'(x_0)(x-x_0) {/eq}

Since the function is defined in implicit form and it cannot be converted to explicit form, the slope of the tangent (derivative)

is found applying the implicit differentiation technique.

## Answer and Explanation:

We are given the implicit equation

{eq}\displaystyle x^2-xy-y^2=1 {/eq}

Diffrentiating the equation with respect to x we find

{eq}\displaystyle...

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#### Learn more about this topic:

from NY Regents Exam - Geometry: Tutoring Solution

Chapter 1 / Lesson 11