Question

How to find the equation of a parabola with 2 points and a linear line?

Answer 1

To find the equation of a parabola using 2 points and a linear line, we go back to the standard form of the parabola which is (y-k)^2 = 4a (x-h)^2 or (x-h)^2 = 4a (y-k)^2 depending on the opening of the parabola. Using two points, we can get relate this to the graph. The linear line lastly has to be the directrix in which it entails equal distance between the focus and the vertex and that of the vertex and the linear line. This should be enough to determine the value of a. In this case, we can now get the expression of the parabolic function.