Answered: Use implicit differentiation to find…

Use implicit differentiation to find the tangent line (in slope intercept form) to the ellipse 4x2 + y? = 12 at the point (-1, 2).

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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Question

Use implicit differentiation to find the tangent line (in slope intercept form) to the ellipse
4x2 + y? = 12 at the point (-1, 2).

Expert Solution

Step 1

Equation of tangent line at a point {say $(x_{0}, y_{0})$ } is

$y - y_{0} = m (x - x_{o}) . . . . (1)$

Where 'm' is slope and 'm' at point $(x_{0}, y_{0})$ is

$m = {(\frac{d y}{d x})}_{(x_{0}, y_{0})}$

Step 2

Given

$4 x^{2} + y^{2} = 12 . . . . (2)$

and

Point (P) $= (- 1, 2)$

Step by step

Solved in 4 steps

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