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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