This general equation in two-degree represents a parabola: $$(ax + by)^2 + 2gx + 2fy + c = 0$$
How do I find the following from this equation:
- Length of Latus Rectum
- Co-ordinates of end points of Latus Rectum
- Equation of Directrix
I know how to find these if a parabola has its axis parallel to either of the co-ordinate axes. But I don't know how to derive these from the general equation.
N.B.: w.r.t. a comment by @Vasya, I produce this picture from my book, where it says that the general form of the equation of a parabola is the above equation. The book gives the equation, but doesn't derive any of the above from the equation: