# 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 a*x* + 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

PF^{2} = e^{2} x (PM)^{2}

(*x* – p)^{2} + (y - q)^{2} = e^{2}. (a*x* + by + c)^{2}

(a^{2} + b^{2})

Simplifying we get;

a*x*^{2} + 2h*x*y + by2 + 2g*x* + 2fy + c = 0

Where, h^{2} < ab

And.

abc + 2gh – af^{2} – bg^{2} – ch^{2} = 0

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### Following are some of the topics in Conic Sections-Parabola, Hyperbola And Ellipse in which we provide help:

- Introduction To Conic Sections
- Eccentricity
- Parameters Of Conic Section
- Parabola
- Forms Of Parabola
- General Equation Of Parabola
- Position Of A Point With Respect To Parabola
- Equation Of A Tangent And Normal At A Point
- Condition Of Tangency
- Point Of Contact Of A Line And A Parabola
- Ellipse
- Ellipse Properties

- Vertical Form Of Ellipse
- General Equation Of Ellipse
- Position Of A Point With Respect To An Ellipse
- Eccentric Angle
- Equations Of Tangent And Normal To An Ellipse
- Condition Of A Line To Touch An Ellipse
- Hyperbola
- Forms Of Hyperbola
- General Equation Of Hyperbola
- Tangent And Normal At A Point On Hyperbola
- Intersection Of A Line And Hyperbola
- Equation Of A Tangent From A Point Outside The Hyperbola

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