Math Assignment 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

PM

PF² = e² x PM²

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

(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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