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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

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√(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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