Implicit Differentiation Problems | 2005 - 2007 | Www.ilearnmath.net

Implicit Differentiation :: 2006-2007 :: Shubleka

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Problem 1 Find an equation of the tangent line to the hyperbola

x2 a2

 by2  1 at the point x0 , y0 . 2

Problem 2 Show by implicit differentiation that the tangent to the ellipse x0 x a2

x2 a2

 by2  1 at the point x0 , y0  is 2

 yb02y  1

Problem 3 Show that the sum of the intercepts of any tangent line to

x  y  c is equal to c.

Problem 4 Find all points on the curve x 2 y 2  xy  2 where the slope of the tangent is equal to -1.