Math Assignment Help With General Equation Of Ellipse

7.6.5 General equation of ellipse:

Let e be the eccentricity of the ellipse having focus F(p, q) and equation of directrix ax + by + c = 0

Let P(x, y) be any point on the ellipse and PM be the perpendicular on the directrix.

Therefore,

PF/PM = e

PF² = e² x (PM)²

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

(a² + b²)

Simplifying we get;

ax² + 2hxy + by2 + 2gx + 2fy + c = 0

Where, h² < ab

And.

abc + 2gh – af² – bg² – ch² = 0

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