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

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(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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