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Math Course Help With General Equation Of Hyperbola

7.6.4 General equation of Hyperbola:

If F(p,q) be the focus and ax + by + c = 0 be the equation of the directrix and e be the eccentricity of the required hyperbola, then P be a point on it with coordinates(x, y). If PM be the length of perpendicular from P on the directrix, then;

PF = e


PF2 = e2 x PM2

(x – p)2 + (y – q)2 = e2. (ax + by + c)2

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(a2 + b2)

ax2 + 2hxy + by2 + 2gx + 2fy + c = 0

This is the general equation of hyperbola

h2 > ab and abc + 2fgh – af2 – bg2 – ch2 ≠ 0

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