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Tangents and Stationary Points to Implicit Curves

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How to find tangents and stationary points to implicit curves?

Finding Tangents to Implicit Curves
Find the equation of the tangent to the curve y2 - 2xy = 3x2 at x = 1, given y > 0.
Finding Stationary Points to Implicit Curves
Find the coordinates of the stationary points for the curve x2 - 4xy = y2 - 20.

Nature of Stationary Points to an implicit curve
A-Level Edexcel C4 January 2009 Q1(b)
Worked solution to this question on implicit differentiation and curves
A curve C has the equation y2 – 3y = x3 + 8.
(a) Find dy/dx in terms of x and y.
(b) Hence find the gradient of C at the point where y = 3

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