Answered: Use implicit differentiation to find…

Use implicit differentiation to find the points where the circle defined by x^2+y^2-2x-4y=4 has horizontal and vertical tangent lines. At what points vertical and horizontal tangent lines

Trigonometry (MindTap Course List)

10th Edition

ISBN:9781337278461

Author:Ron Larson

Publisher:Ron Larson

Chapter6: Topics In Analytic Geometry

Section6.2: Introduction To Conics: parabolas

Problem 4ECP: Find an equation of the tangent line to the parabola y=3x2 at the point 1,3.

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Concept explainers

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:

Question

Use implicit differentiation to find the points where the circle defined by

x^2+y^2-2x-4y=4

has horizontal and vertical tangent lines.

At what points vertical and horizontal tangent lines

With integration, one of the major concepts of calculus. Differentiation is the derivative or rate of change of a function with respect to the independent variable.

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Given,

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Now the tangent line is horizontal if slope of the tangent is zero.

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Now the tangent line is vertical if

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