**7.5.1 Introduction: **A parabola is the locus of all points in a plane equidistant from a fixed point, called the focus, and a fixed straight line, called the directrix.

In the parabola shown in figure 2-8, point V, which lies halfway between the focus and the directrix, is called the vertex of the parabola. In this figure and in many of the parabolas discussed in the first portion of this section, the vertex of the parabola falls at the origin; however, the vertex of the parabola, like the center of the circle, can fall at any point in the plane.

**7.5.2 Standard equation of Parabola:**

Take a point F(a, 0) as the focus, where a> 0.

A line D with equation *x *= -a is taken as directrix.

Let P(*x*, y) be a point on locus and PM is the perpendicular on the directrix.

Then,

PF = PM

PF^{2} = PM^{2}

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

y^{2} = (*x* + a)^{2} – (*x* – a)^{2}

y^{2} = 4a*x*

this is the standard equation of parabola.

Focus = F(a, 0)

Vertex = O(0, 0)

Equation of axis; y = 0

Equation of directrix; *x* + a = 0

**To Schedule a Parabola tutoring session
To submit Parabola 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