**7.1 Introduction: **A conic section is the intersection of a plane and a cone. Hyperbola, ellipse and parabola are together known as conic sections, or just conics. They are so called because they are formed by the intersection of a right circular cone and a plane.

**The General Equation for a Conic Section:**

**A x^{2} + Bxy + Cy^{2} + Dx + Ey + F = 0**

**7.2 Types of conics: **There are three types of conics, hyperbola, ellipse, and parabola. The circle can be considered as a fourth type or as a kind of ellipse.

i) The circle and the ellipse are generated when the intersection of cone and plane is a closed curve.

ii) The circle is obtained when the cutting plane is parallel to the plane of the generating circle of the cone -- for a right cone as in the picture at the top of the page this means that the cutting plane is perpendicular to the symmetry axis of the cone.

iii) If the cutting plane is parallel to exactly one generating line of the cone, then the conic is unbounded and is called a parabola.

iv) In the remaining cases, the figure is a hyperbola. In this case, the plane will intersect both halves of the cone, producing two separate unbounded curves

The type of sections can be found by using the formula;

**B ^{2}– 4AC**

- If B
^{2}– 4AC > 0, then, the curve is a circle, ellipse, point or no curve. - If B
^{2}– 4AC = 0, then, the curve is a parabola, two parallel lines, 1 line or no curve. - If B
^{2}– 4AC < 0, then the curve is a hyperbola or two intersecting lines.

Through change of coordinates these equations can be put in standard forms:

- Circle:
*x*^{2}+ y^{2}= r^{2} - Ellipse:
*x*2/a2 + y2/b2 = 1 ,*x*^{2}/a2 y^{2}/b2 = 1 - Parabola: y
^{2}= 4a*x*,*x*^{2}= 4ay, - Hyperbola:
*x*^{2}/a2 ̲ y^{2}/b2 = 1,*x*^{2}/a2 ̲ y^{2}/b2 = -1 - Rectangular Hyperbola:
*x*y = c^{2}

Such forms will be symmetrical about the *x*-axis and for the circle, ellipse and hyperbola symmetrical about the *y*-axis.

The rectangular hyperbola however is only symmetrical about the lines *y* = *x* and *y* = − *x*. Therefore its inverse function is exactly the same as its original function.

These standard forms can be written as parametric equations,

- Circle: (acosθ,asinθ),
- Ellipse: (acosθ, bsinθ),
- Parabola: (at2, 2at),
- Hyperbola: (asecθ, btanθ) or (± a cosh u, b sinh u)
- Rectangular Hyperbola: (ct, c/t)

**To Schedule a Conic Sections-Parabola, Hyperbola And Ellipse tutoring session
To submit Conic Sections-Parabola, Hyperbola And 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

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 help
- College Essay Writing
- Cheap Essay Writing