Question

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Answer 1

Question-----> If , ( x - a )² + ( y - b )² = c² , prove that ,

[ 1 + ( dy/dx )² ]³/² / ( d²y/dx² ) is a constant ie independent of a and b .

Solution-----> 1 ) Plzzz refer the attachment

2) First we differentiate the given equation and find dy/dx by using,

d/dx ( xⁿ ) = n xⁿ⁻¹

3) Then we differentiate dy/dx , again by using , division rule of differentiation.

d/dx ( u/v ) = ( v du/dx - u dv/dx ) / v²

and putting ( x - a )² + ( y - b )² = c² and get ,

d²y/dx² = - c² / ( y - b )³

4) Then we calculate value of given expression by putting value of dy/dx and d²y/dx²⃗ and by solving we get, -C , which is constant independent of a and b .

Answer 2

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