SOLUTION: Find the slope of the tangent line: (a)To the ellipse x^2+y^2/2=1 at the point (1/√2,1) (b)To the hyperbola x^2−y^2=1 at the point (√3,√2)

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Question 825587: Find the slope of the tangent line:
(a)To the ellipse x^2+y^2/2=1 at the point (1/√2,1)
(b)To the hyperbola x^2−y^2=1 at the point (√3,√2)

Answer by AnlytcPhil(1807)   (Show Source): You can put this solution on YOUR website!
Find the slope of the tangent line:
 (a)To the ellipse x^2+y^2/2=1 at the point (1/√2,1) 
 (b)To the hyperbola x^2−y^2=1 at the point (√3,√2) 

The slope of the tangent line at a point IS the derivative
at that point.



Clear of fractions by multiplying through by 2



Take the derivative term-by-term implicitly:



 is just 1 so



Subtract 4x from both sides:



Divide both sides by 2y





So we substitute the point (,1)

@(,1) 

The other one is done the same way.

Edwin
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