# Satisfy the parabola when point (A, B) and the equation is given

Given a point **(A, B)** such that distance from each point on the curve **M.y = N.x ^{2} + O.x + P** with

**(A, B)**is equal to the distance between that point on the curve and

**x-axis**. The task is to find the value of

**M, N O and P**.

**Note:** The equation should be in simple form i.e. **gcd( |M|, |N|, |O|, |P| ) = 1** and **N** should always be positive.

**Examples:**

Input:A = 1, B = 1Output:2 1 -2 2

M = 2, N = 1, O = -2, P = 2

The equation of the curve will be2y = x^{2}– 2x + 2

Input:A = -1, B = 1Output:2 1 2 2

**Approach:** From the property of the parabola, for every point on the curve the distance with the directrix and the focus will always be equal. Using this property, consider **y = 0** as a directrix and **(A, B)** as the focus.

Since in the equation **N** is given to be always positive, the parabola will be facing upward and the equation of the parabola is **(x – h) ^{2} = 4p(y – k)** where

**(h, k)**is the co-ordinate of the vertex and p is the distance between focus and vertex or vertex and directrix.

Since the vertex is the mid point between the perpendicular distance form focus **(A, B)** and the directrix here (A, 0) is **B**. So the co-ordinate of the vertex is (A, B/2) and **p** is also **B/2**.

So, the equation will be **(x – A) ^{2} = 4 * B/2 * (y – B/2)**.

This equation can be solved to get the result:

Below is the implementation of the above approach:

## C++

`// C++ implementation of the approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to find the required values` `void` `solve(` `int` `A, ` `int` `B)` `{` ` ` `double` `p = B / 2.0;` ` ` `int` `M = ` `ceil` `(4 * p);` ` ` `int` `N = 1;` ` ` `int` `O = - 2 * A;` ` ` `int` `Q = ` `ceil` `(A * A + 4 * p*p);` ` ` `cout << M << ` `" "` `<< N << ` `" "` ` ` `<< O << ` `" "` `<< Q;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `a = 1;` ` ` `int` `b = 1;` ` ` `solve(a, b);` `}` `// This code is contributed by Mohit Kumar` |

## Java

`// Java implementation of the approach` `class` `GFG` `{` ` ` ` ` `// Function to find the required values` ` ` `static` `void` `solve(` `int` `A, ` `int` `B)` ` ` `{` ` ` `double` `p = B / ` `2.0` `;` ` ` `double` `M = Math.ceil(` `4` `* p);` ` ` `int` `N = ` `1` `;` ` ` `int` `O = - ` `2` `* A;` ` ` `double` `Q = Math.ceil(A * A + ` `4` `* p * p);` ` ` `System.out.println(M + ` `" "` `+ N +` ` ` `" "` `+ O + ` `" "` `+ Q);` ` ` `}` ` ` ` ` `// Driver code` ` ` `public` `static` `void` `main (String[] args)` ` ` `{` ` ` `int` `a = ` `1` `;` ` ` `int` `b = ` `1` `;` ` ` `solve(a, b);` ` ` `}` `}` `// This code is contributed by AnkitRai01` |

## Python3

`# Python3 implementation of the approach` `# Function to find the required values` `def` `solve(A, B):` ` ` `p ` `=` `B ` `/` `2` ` ` `M ` `=` `int` `(` `4` `*` `p)` ` ` `N ` `=` `1` ` ` `O ` `=` `-` `2` `*` `A` ` ` `Q ` `=` `int` `(A ` `*` `A ` `+` `4` `*` `p` `*` `p)` ` ` `return` `[M, N, O, Q]` `# Driver code` `a ` `=` `1` `b ` `=` `1` `print` `(` `*` `solve(a, b))` |

## C#

`// C# implementation of the approach` `using` `System;` `class` `GFG` `{` ` ` `// Function to find the required values` ` ` `static` `void` `solve(` `int` `A, ` `int` `B)` ` ` `{` ` ` `double` `p = B / 2.0;` ` ` ` ` `double` `M = Math.Ceiling(4 * p);` ` ` ` ` `int` `N = 1;` ` ` `int` `O = - 2 * A;` ` ` ` ` `double` `Q = Math.Ceiling(A * A + 4 * p * p);` ` ` ` ` `Console.Write(M + ` `" "` `+ N + ` `" "` `+ O + ` `" "` `+ Q);` ` ` `}` ` ` ` ` `// Driver code` ` ` `static` `public` `void` `Main ()` ` ` `{` ` ` `int` `a = 1;` ` ` `int` `b = 1;` ` ` `solve(a, b);` ` ` `}` `}` `// This code is contributed by AnkitRai01` |

## Javascript

`<script>` ` ` `// JavaScript implementation of the approach` ` ` ` ` `// Function to find the required values` ` ` `function` `solve(A, B)` ` ` `{` ` ` `let p = B / 2.0;` ` ` `let M = Math.ceil(4 * p);` ` ` `let N = 1;` ` ` `let O = - 2 * A;` ` ` `let Q = Math.ceil(A * A + 4 * p * p);` ` ` `document.write(M + ` `" "` `+ N + ` `" "` `+ O + ` `" "` `+ Q);` ` ` `}` ` ` ` ` `let a = 1;` ` ` `let b = 1;` ` ` `solve(a, b);` ` ` `</script>` |

**Output:**

2 1 -2 2

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