Check if a point is inside, outside or on the ellipse in C++

Suppose, one ellipse is given (the center coordinate (h, k) and semi-major axis a, and semi-minor axis b), another point is also given. We have to find whether the point is inside the ellipse or not. To solve it, we have to solve the following equation for the given point (x, y).

$$\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}\leq1$$

If the result is less than one, then the point is inside the ellipse, otherwise not.

Example

 Live Demo

#include <iostream>
#include <cmath>
using namespace std;
bool isInsideEllipse(int h, int k, int x, int y, int a, int b) {
   int res = (pow((x - h), 2) / pow(a, 2)) + (pow((y - k), 2) / pow(b, 2));
   return res;
}
int main() {
   int x = 2, y = 1, h = 0, k = 0, a = 4, b = 5;
   if(isInsideEllipse(h, k, x, y, a, b) > 1){
      cout <<"Outside Ellipse";
   }
   else if(isInsideEllipse(h, k, x, y, a, b) == 1){
      cout <<"On the Ellipse";
   } else{
      cout <<"Inside Ellipse";
   }
}

Output

Inside Ellipse

Arnab Chakraborty

Published on 22-Oct-2019 06:40:32

• Related Questions & Answers
• Check if a point is inside, outside or on the parabola in C++
• Check if a point lies on or inside a rectangle in Python
• C++ Program to Check if a Point d lies inside or outside a circle defined by Points a, b, c in a Plane
• Check if a given point lies inside a Polygon
• Check if points are inside ellipse faster than contains_point method (Matplotlib)
• Find if a point lies inside a Circle in C++
• JavaScript variables declare outside or inside loop?
• Check if a circle lies inside another circle or not in C++
• Check whether a given point lies inside a Triangle
• Check if a number is jumbled or not in C++
• Check if a Tree is Isomorphic or not in C++
• Program to check given point in inside or boundary of given polygon or not in python
• Check if Input, Output and Error is redirected on the Console or not in C#
• What's the fastest way of checking if a point is inside a polygon in Python?
• Check if a directed graph is connected or not in C++