A parabola starts at a coordinate A and ends at coordinate B. Angel of tangent through A is given 'theta'. With these data (A,B,theta) how can I get an equation of a parabola?
2026-04-13 10:43:07.1776076987
Equation of parabola from 2 points and an angle at the first point
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You have to construct a system of simultaneous equations. Let $A(x_1,y_1)$ and $B(x_2,y_2)$ the equation of parabola is polynomial of degree $2$ say $y=ax^2+bx+c$ so you can substitute at first $x=x_1 , y=y_1$ then $x=x_2 , y=y_2$ now you have tow equation the third equation will be find from $\tan \theta=y'=2ax+b$