Mathematics

Problem

The ellipse

9x^2 + 16y^2 = 144

is given. a. (i) Obtain

\dfrac{dy}{dx}

in terms of

x

and

y

. b. (ii) The tangent to the ellipse has slope

-\dfrac{3}{4}

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

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