Given a parabola with vertex (h, k), and
Examples:
Input: h = 100, k = 500, x = 20, y = 10, a = 4 Output: Outside Input: h = 0, k = 0, x = 2, y = 1, a = 4 Output: Inside
Approach: It is very simple, we have to just solve the equation for point (x, y):
(y-k)^2 = 4a(x-h)
or, (y-k)^2 – 4a(x-h) = 0
After solving, if the result comes less than 0 then the point lies within, else if it comes exact 0 then the point lies on the parabola, and if the result is greater than 0 unsatisfied the point lies outside of the parabola.
Here we are taking a parabola whose axis of symmetry is y = k, although the approach is applicable for any parabola.
Below is the implementation of above approach:
// C++ Program to check if the point // lies within the parabola or not #include <bits/stdc++.h> using namespace std;
// Function to check the point int checkpoint( int h, int k, int x, int y, int a)
{ // checking the equation of
// parabola with the given point
int p = pow ((y - k), 2) - 4 * a * (x - h);
return p;
} // Driver code int main()
{ int h = 0, k = 0, x = 2, y = 1, a = 4;
if (checkpoint(h, k, x, y, a) > 0)
cout << "Outside" << endl;
else if (checkpoint(h, k, x, y, a) == 0)
cout << "On the parabola" << endl;
else
cout << "Inside" << endl;
return 0;
} |
// Java Program to check if the point // lies within the parabola or not class solution
{ // Function to check the point static int checkpoint( int h, int k, int x, int y, int a)
{ // checking the equation of
// parabola with the given point
int p =( int ) Math.pow((y - k), 2 ) - 4 * a * (x - h);
return p;
} //driver code public static void main(String arr[])
{ int h = 0 , k = 0 , x = 2 , y = 1 , a = 4 ;
if (checkpoint(h, k, x, y, a) > 0 )
System.out.println( "Outside" );
else if (checkpoint(h, k, x, y, a) == 0 )
System.out.println( "On the parabola" );
else
System.out.println( "Inside" );
} } |
# Python3 Program to check if the point # lies within the parabola or not # Function to check the point def checkpoint(h, k, x, y, a):
# checking the equation of
# parabola with the given point
p = pow ((y - k), 2 ) - 4 * a * (x - h)
return p
# Driver code if __name__ = = "__main__" :
h = 0
k = 0
x = 2
y = 1
a = 4
if checkpoint(h, k, x, y, a) > 0 :
print ( "Outside\n" )
elif checkpoint(h, k, x, y, a) = = 0 :
print ( "On the parabola\n" )
else :
print ( "Inside\n" );
# This code is contributed by # Surendra_Gangwar |
// C# Program to check if the point // lies within the parabola or not using System;
class GFG
{ // Function to check the point public static int checkpoint( int h, int k,
int x, int y,
int a)
{ // checking the equation of
// parabola with the given point
int p = ( int ) Math.Pow((y - k), 2) -
4 * a * (x - h);
return p;
} // Driver code public static void Main( string [] arr)
{ int h = 0, k = 0,
x = 2, y = 1, a = 4;
if (checkpoint(h, k, x, y, a) > 0)
{
Console.WriteLine( "Outside" );
}
else if (checkpoint(h, k, x, y, a) == 0)
{
Console.WriteLine( "On the parabola" );
}
else
{
Console.WriteLine( "Inside" );
}
} } // This code is contributed // by Shrikant13 |
<?php // PHP Program to check if // the point lies within // the parabola or not // Function to check the point function checkpoint( $h , $k , $x ,
$y , $a )
{ // checking the equation of
// parabola with the given point
$p = pow(( $y - $k ), 2) - 4 *
$a * ( $x - $h );
return $p ;
} // Driver code $h = 0; $k = 0; $x = 2;
$y = 1; $a = 4;
if (checkpoint( $h , $k , $x ,
$y , $a ) > 0)
echo "Outside" ;
else if (checkpoint( $h , $k , $x ,
$y , $a ) == 0)
echo "On the parabola" ;
else echo "Inside" ;
// This code is contributed // by inder_verma ?> |
<script> // javascript Program to check if the point // lies within the parabola or not // Function to check the point function checkpoint(h , k , x , y , a)
{ // checking the equation of
// parabola with the given point
var p =parseInt(Math.pow((y - k), 2) - 4 * a * (x - h));
return p;
} //driver code var h = 0, k = 0, x = 2, y = 1, a = 4;
if (checkpoint(h, k, x, y, a) > 0)
document.write( "Outside" );
else if (checkpoint(h, k, x, y, a) == 0)
document.write( "On the parabola" );
else document.write( "Inside" );
// This code is contributed by 29AjayKumar </script> |
Output:
Inside
Time Complexity: O(1)
Auxiliary Space: O(1)