**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

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- 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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