Given a curve [ y = x(A – x) ], the task is to find normal at given point ( x, y) on that curve, here A is any integer number and x, y also any integer.
Input: A = 2, x = 2, y = 0 Output: 2y = x - 2 Since y = x(2 - x) y = 2x - x^2 differentiate it with respect to x dy/dx = 2 - 2x put x = 2, y = 0 in this equation dy/dx = 2 - 2* 2 = -2 equation => (Y - 0 ) = ((-1/-2))*( Y - 2) => 2y = x -2 Input: A = 3, x = 4, y = 5 Output: Not possible Point is not on that curve
Approach: First we need to find given point is on that curve or not if the point is on that curve then:
- We need to differentiate that equation that point don’t think too much for differentiation of this equation if you analyze then you find that dy/dx always become A – 2x.
- Put x, y in dy/dx.
- Equation of normal is Y – y = -(1/( dy/dx )) * (X – x).
Below is the implementation of the above approach:
2y = x-2
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