**7.7.1 Introduction:**In mathematics a hyperbola is a smooth planar curve having two connected components or branches, each being a mirror image of the other and resembling two infinite bows aimed at each other as seen in the figure below. The hyperbola is traditionally described as one of the kinds of conic section or intersection of a plane and a cone, namely when the plane makes a smaller angle with the axis of the cone than does the cone itself , the other kinds being the parabola and the ellipse (including the circle).

A hyperbola is the locus of a point that moves in such a way that the ratio of its distance from a fixed point (known as focus) to its distance from a fixed line(called the directrix) equals a constant e > 1.

7.7.2 Equation of standard form of Hyperbola: F(c, 0) and F’(c, 0) are the two fixed points, where c > 0. Let P(x, y) be any point on the locus of all points, the difference of whose distances from F and F’ is a positive constant, 2a, where 0 < a < c

|PF – PF’| = 2a

PF – PF’ = ± 2a

√(*x* – c)^{2} + y^{2} - √(*x* + c)^{2} + y^{2} = ± 2a

√(*x* + c)^{2} + y^{2} = √(*x* – c)^{2} + y^{2} ± 2a

(*x* + c)^{2} + y^{2} = (*x* – c)^{2} + y^{2} + 4a^{2} ± 4a √(*x* – c)^{2} + y^{2}

4c*x* – 4a^{2} = ± 4a√(*x* – c)^{2} + y2

(c/a)*x* – a = ± √(*x* – c)^{2} + y^{2}

(c^{2}/a^{2}) *x*^{2} + a^{2} – 2c*x* = (*x* – c)^{2} + y^{2}

c^{2} – 1 *x*^{2} – y^{2} = (c^{2} – a^{2})

(c^{2} – a^{2})*x*^{2} – a^{2}y^{2} = a^{2}(c^{2} – a^{2})

*x*^{2}-y^{2} = 1

*x*^{2} **-y ^{2} = 1 **

**a ^{2} b^{2} **

where b^{2} = c^{2} – a^{2}

this is the standard equation of hyperbola.

Length of transverse axis = AA’ = 2a

Length of conjugate axis = 2b

Eccentricity = e = (√a^{2} + b^{2})/ a

**To Schedule a Position of A Point With Respect To An Ellipse tutoring session
To submit Position of A Point With Respect To An Ellipse assignment click here.**

- 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

Assignment Writing Help

- Science Assignment Help
- Math Assignment Help
- Chemistry Assignment Help
- Physics Assignment Help
- Biology Assignment Help
- Psychology Assignment Help
- History Assignment Help
- Geography Assignment Help
- English Assignment Help
- Humanities Assignment Help
- Nursing Assignment Help
- Social Science Assignment Help
- Arts and Architecture Help
- Statistics Assignment Help
- Law Assignment Help
- Computational Mathematics Assignment Help

Engineering Assignment Services

- Programming Assignment Help
- Database Help
- Data Structure Assignment Help
- Operating Systems Assignment Help
- Computer Network Assignment Help
- UML Diagram Assignment Help
- IT Assignment Help
- Game Programming Help
- Computer Science Assignment Help
- Information Systems Assignment Help
- Chemical Engineering Assignment Help
- Civil Engineering Assignment Help
- Electrical, Electronics Help
- Mechanical Engineering Assignment Help
- Petroleum Engineering Assignment Help
- Biochemical and Biotechnology Help

Do My Assignment Help

- Accounting Assignment Help
- Finance Assignment Help
- Economics Assignment Help
- Marketing Assignment Help
- Human Resources Assignment Help
- Operations Management Assignment Help
- Strategy and Planning Help
- Project Management Help
- Case Studies Writing Help
- Political science
- Referencing Help
- Assignment Help Websites
- Online Assignment Help
- Do My Assignment
- Do My Homework
- Health Informatics

Write My Essay Services

- Essay Writing Help
- Business Essay Writing Help
- Assignment Writing Services
- Plagiarism Free Essay Writing
- Essay Editing Service
- Dissertation Writing Services
- Thesis Writing Help
- Custom Writing Help
- Write My Essay
- Write My Paper
- Paper Writing Service
- Academic Writing Help
- College Essay Writing
- Cheap Essay Writing