The ellipse is given.

MATHEMATICS · Multi-part · AP · Calculus AB · Differentiation: Composite, Implicit, and Inverse Functions · Differentiation: Composite, Implicit, and Inverse Functions

Problem

The ellipse

9x^2 + 16y^2 = 144

is given. (i) Obtain

\dfrac{dy}{dx}

in terms of

x

and

y

. (ii) The tangent to the ellipse has slope

-\dfrac{3}{4}

. Find all points on the ellipse where this occurs. (iii) For each point obtained in part (ii), write the equation of the corresponding tangent line.

Related theory

Ellipse
Conic Sections
Advanced Differentiation
Coordinate Geometry
Ellipse standard equation

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