A set of points on a plain surface that forms a curve such that any point on that curve is equidistant from the focus is a parabola.
Vertex of a parabola is the coordinate from which it takes the sharpest turn whereas a is the straight line used to generate the curve.
The standard form of a parabola equation is . Given the values of a, b and c; our task is to find the coordinates of vertex, focus and the equation of the directrix.
Example –
Input : 5 3 2 Output : Vertex:(-0.3, 1.55) Focus: (-0.3, 1.6) Directrix: y=-198 Consult the formula below for explanation.
Recommended: Please try your approach on {IDE} first, before moving on to the solution.
// Java program to calculate Vertex, Focus and Directrix public class TriangularPyramidNumber { public static void parabola( float a, float b, float c) { System.out.println( "Vertex: (" + (-b / ( 2 * a)) + ", " + ((( 4 * a * c) - (b * b)) / ( 4 * a)) + ")" ); System.out.println( "Focus: (" + (-b / ( 2 * a)) + ", " + ((( 4 * a * c) - (b * b) + 1 ) / ( 4 * a)) + ")" ); System.out.println( "Directrix: y=" + ( int )(c - ((b * b) + 1 ) * 4 * a)); } public static void main(String[] args) { float a = 5 , b = 3 , c = 2 ; parabola(a, b, c); } } // Contributed by _omg |
Vertex: (-0.3, 1.55) Focus: (-0.3, 1.6) Directrix: y=-198
Please refer complete article on Finding the vertex, focus and directrix of a parabola for more details!