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
- Find Tangent at a given point on the curve
- Find nth term of the Dragon Curve Sequence
- Program to find Normal and Trace of a matrix
- Find the other end point of a line with given one end and mid
- Program to find the mid-point of a line
- Find the Missing Point of Parallelogram
- Program to find the Break Even Point
- Find a point that lies inside exactly K given squares
- Find mirror image of a point in 2-D plane
- Find if a point lies inside a Circle
- Find the foot of perpendicular of a point in a 3 D plane
- Program to find GCD of floating point numbers
- Find a point such that sum of the Manhattan distances is minimized
- Find an Integer point on a line segment with given two ends
- Find the number of points that have atleast 1 point above, below, left or right of it
If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to email@example.com. See your article appearing on the GeeksforGeeks main page and help other Geeks.
Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.