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Use calculus to find the condition that line xcos∂+ysin∂=p is a normal to the curve b 2 x 2 +a 2 y 2 =a 2 b 2

Use calculus to find the condition that line xcos∂+ysin∂=p is a normal to the curve b2x2+a2y2=a2b2

Grade:12th pass

1 Answers

abhay gupta
askIITians Faculty 199 Points
3 years ago
Dear student
Here’s your solution how to solve this

if you differentitate both the equation to find dy/dx i.e. slope of the line
then you can use the theorem, product of slope of perpendicuar lines is -1
i.e. (dy/dx)line 1x (dy/dx)line 2= -1
here (dy/dx)line1= -cot(delta)
and (dy/dx)line 2= (-xb2)/(ya2)

Condition :- xb2.cot(delta) = -ya2

Askiitians expert
Ankit

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