Python Program for Finding the vertex, focus and directrix of a parabola
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.
# Python program to calculate Vertex, Focus and Directrix def parabola(a, b, c): print ( "Vertex: (" , ( - b / ( 2 * a)) , ", " ,((( 4 * a * c) - (b * b)) / ( 4 * a)) , ")" ) print ( "Focus: (" , ( - b / ( 2 * a)) , ", " , ((( 4 * a * c) - (b * b) + 1 ) / ( 4 * a)) , ")" ) print ( "Directrix: y=" , ( int )(c - ((b * b) + 1 ) * 4 * a )) # main() a = 5 b = 3 c = 2 parabola(a, b, c) # Contributed by _omg |
Output :
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!