# Math Course Help With General Equation Of Hyperbola

## 7.6.4 General equation of Hyperbola:

If F(p,q) be the focus and a*x* + 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

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

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

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

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

This is the general equation of hyperbola

h^{2} > ab and abc + 2fgh – 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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