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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Tangent Line: Definition & Equation

from NY Regents Exam - Geometry: Tutoring Solution

Chapter 1 / Lesson 11
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