# Math Assignment Help With Forms of Hyperbola

## 7.6.3 Forms of Hyperbola:

**i) Rectangular Hyperbola:**A hyperbola having equal axes is said to be rectangular hyperbola. i.e.

**2b = 2a or b = a**

In this case the equation of hyperbola is given as;

*x*^{2} – y^{2} = a^{2}

- ii)
**Vertical form of Hyperbola:**

The foci are taken at F(0,c) and F’ (0, -c), the equation of the hyperbola is of the form;

*x*^{2} ‗ y^{2} = 1, where b = √(c^{2} – a^{2})

a^{2} b^{2}

The equation of the vertical form of hyperbola is

*xi2 – yi2* = a2

Points to remember:

- i) Foci F(ae, 0) & F’(-ae, 0)
- ii) Centre O(0,0)
- iii) Length of transverse axis = 2a
- iv) Length of conjugate axis = 2b
- v) Equations of directrices =
*x*= ± (a/e) - vi) Vertices are A(a,0) & A’ (-a,0)
- vii) Eccentricity = e = √(a
^{2}+ b^{2})/a

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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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