Use implicit differentation to find an equation of the tangent line to the curve 2 ( x power to the 2 + y power to the 2 ) power to the 2 = 25 ( x power to the 2 − y power to the 2 ) at the point (3, 1). This line intersects the point (16, b) for some b. Enter the value of b.

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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Use implicit differentation to find an equation of the tangent line to the curve 2 ( x power to the 2 + y power to the 2 ) power to the 2 = 25 ( x power to the 2 − y power to the 2 ) at the point (3, 1).

This line intersects the point (16, b) for some b. Enter the value of b.

Expert Solution
Step 1

Given : 

The function  2 ( x2+y2 ) 2 = 25 ( x2- y2  ) .

 

To find : 

(1) The tangent line of 2 ( x2+y2 ) 2 = 25 ( x2 -y2  )  at the point ( 3 , 1 ) using implicit differentiation.

 

(2) The value of  " b " if (16 , b ) is a point on the tangent line.

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