Dada una curva [ y = x(A – x) ], la tarea es encontrar la tangente en el punto dado (x, y) en esa curva, donde A, x, y son números enteros.
Ejemplos:
Input: A = 2, x = 2, y = 0
Output: y = -2x - 4
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 ) = ((-2))*( Y - 2)
=> y = -2x -4
Input: A = 3, x = 4, y = 5
Output: Not possible
Point is not on that curve
Acercarse:
- Primero encuentre si el punto dado está en esa curva o no.
- Si el punto está en esa curva, encuentra la derivada
- Calcule el gradiente de la tangente Poniendo x, y en dy/dx.
- Determine la ecuación de la tangente sustituyendo el gradiente de la tangente y las coordenadas del punto dado en la forma de punto de gradiente de la ecuación de la línea recta, donde la ecuación de normal es Y – y = ( dy/dx ) * (X – X).
C++
// C++ program for find Tangent
// on a curve at given point
#include <bits/stdc++.h>
using namespace std;
// function for find Tangent
void findTangent(int A, int x, int y)
{
// differentiate given equation
int dif = A - x * 2;
// check that point on the curve or not
if (y == (2 * x - x * x)) {
// if differentiate is negative
if (dif < 0)
cout << "y = "
<< dif << "x" << (x * dif) + (y);
else if (dif > 0)
// differentiate is positive
cout << "y = "
<< dif << "x+" << -x * dif + y;
// differentiate is zero
else
cout << "Not possible";
}
}
// Driver code
int main()
{
// declare variable
int A = 2, x = 2, y = 0;
// call function findTangent
findTangent(A, x, y);
return 0;
}
Java
// Java program for find Tangent
// on a curve at given point
import java.util.*;
import java.lang.*;
import java.io.*;
class GFG
{
// function for find Tangent
static void findTangent(int A, int x, int y)
{
// differentiate given equation
int dif = A - x * 2;
// check that point on the curve or not
if (y == (2 * x - x * x)) {
// if differentiate is negative
if (dif < 0)
System.out.println( "y = "
+ dif + "x" + (x * dif + y));
else if (dif > 0)
// differentiate is positive
System.out.println( "y = "
+ dif + "x+" + -x * dif + y);
// differentiate is zero
else
System.out.println("Not possible");
}
}
// Driver code
public static void main(String args[])
{
// declare variable
int A = 2, x = 2, y = 0;
// call function findTangent
findTangent(A, x, y);
}
}
Python3
# Python3 program for find Tangent
# on a curve at given point
# function for find Tangent
def findTangent(A, x, y) :
# differentiate given equation
dif = A - x * 2
# check that point on the curve or not
if y == (2 * x - x * x) :
# if differentiate is negative
if dif < 0 :
print("y =",dif,"x",(x * dif) + (y))
# differentiate is positive
elif dif > 0 :
print("y =",dif,"x+",-x * dif + y)
# differentiate is zero
else :
print("Not Possible")
# Driver code
if __name__ == "__main__" :
# declare variable
A, x, y = 2, 2, 0
# call function findTangent
findTangent(A, x, y)
# This code is contributed by
# ANKITRAI1
C#
// C# program for find Tangent
// on a curve at given point
using System;
class GFG
{
// function for find Tangent
static void findTangent(int A, int x, int y)
{
// differentiate given equation
int dif = A - x * 2;
// check that point on the curve or not
if (y == (2 * x - x * x)) {
// if differentiate is negative
if (dif < 0)
Console.Write( "y = "
+ dif + "x" + (x * dif + y)+"\n");
else if (dif > 0)
// differentiate is positive
Console.Write( "y = "
+ dif + "x+" + -x * dif + y+"\n");
// differentiate is zero
else
Console.Write("Not possible"+"\n");
}
}
// Driver code
public static void Main()
{
// declare variable
int A = 2, x = 2, y = 0;
// call function findTangent
findTangent(A, x, y);
}
}
PHP
<?php
// PHP program for find Tangent
// on a curve at given point
// function for find Tangent
function findTangent($A, $x, $y)
{
// differentiate given equation
$dif = $A - $x * 2;
// check that point on the
// curve or not
if ($y == (2 * $x - $x * $x))
{
// if differentiate is negative
if ($dif < 0)
echo "y = ", $dif , "x" ,
($x * $dif) + ($y);
else if ($dif > 0)
// differentiate is positive
echo "y = ",
$dif , "x+" , -$x * $dif + $y;
// differentiate is zero
else
echo "Not possible";
}
}
// Driver code
// declare variable
$A = 2;
$x = 2;
$y = 0;
// call function findTangent
findTangent($A, $x, $y);
// This code is contributed by Sachin
?>
Javascript
<script>
// javascript program for find Tangent
// on a curve at given point
// function for find Tangent
function findTangent( A, x, y)
{
// differentiate given equation
var dif = A - x * 2;
// check that point on the curve or not
if (y == (2 * x - x * x)) {
// if differentiate is negative
if (dif < 0)
document.write( "y = "
+ dif + "x" + (x * dif + y)+"\n");
else if (dif > 0)
// differentiate is positive
document.write( "y = "
+ dif + "x+" + -x * dif + y+"\n");
// differentiate is zero
else
document.write("Not possible"+"\n");
}
}
// Driver code
// declare variable
var A = 2, x = 2, y = 0;
// call function findTangent
findTangent(A, x, y);
// This code is contributed by bunnyram19.
</script>
Producción:
y = -2x-4
Complejidad de tiempo: O (1), ya que no estamos usando ningún bucle.
Espacio auxiliar: O (1), ya que no estamos usando ningún espacio adicional.