Math Assignment Help With General Equation Of Parabola

7.5.4 General equation of parabola:

Let F(h, k) be the focus of the parabola and let the equation of its directrix be;

Ax + by + c = 0

Let P(x, y) be a point on the parabola and PM be the perpendicular from P on the directrix.

PF = PM

√(x – h)² + (y – k)² = ax + by + c

√(a² + b²)

x – h)² + (y – k)² = (ax + by + c)²

a² + b²

(a² + b²) [(x – h)² + (y – k)²] = (ax + by + c)²

On solving the above equation we get;

(bx – ay)² + 2gx + 2fy + d = 0

This is the general form of parabolic equation.

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