# Parabola

## Focus of Parabola Coordinates with Examples

Here you will learn how to find the focus of parabola with examples. Let’s begin – Focus of Parabola Coordinates (i) For Parabola $$y^2$$ = 4ax : The coordinates of focus is (a, 0). (ii) For Parabola $$y^2$$ = -4ax : The coordinates of focus is (-a, 0). (iii) For Parabola $$x^2$$ = 4ay : …

## Directrix of Parabola – Equation and Formula

Here you will learn formula for finding the equation of directrix of parabola with examples. Let’s begin – Equation of Directrix of Parabola (i) For Parabola $$y^2$$ = 4ax : The equation of directrix is x = -a. (ii) For Parabola $$y^2$$ = -4ax : The equation of directrix is x = a. (iii) For …

## Length of Latus Rectum of Parabola Formula

Here you will learn formula to find the length of latus rectum of parabola with examples. Let’s begin – Latus Rectum of Parabola A double ordinate through the focus is called the latus rectum i.e. the latus rectum of a parabola is a chord passing through the focus perpendicular to the axis. In the given …

## Parametric Equation of all Forms of Parabola

Here you will learn what is the parametric equation of all forms of parabola and their parametric coordinates. Let’s begin – Parametric Equation of Parabola and Coordinates (i) For the parabola $$y^2$$ = 4ax : The parametric equation is x = $$at^2$$ & y = 2at. And parametric coordinates are ($$at^2$$, 2at). (ii) For the …

## Parabola Examples

Here you will learn some parabola examples for better understanding of parabola concepts. Example 1 : The length of latus rectum of a parabola, whose focus is (2, 3) and directrix is the line x – 4y + 3 = 0 is – Solution : The length of latus rectum = 2 x perp. from …

## Different Types of Parabola Equations

Here, you will learn Different Types of Parabola and Standard equations of parabola, focal chord, double ordinate and latus rectum of parabola. Let’s begin – What is Parabola ? A parabola is the locus of a point which moves in a plane, such that its distance from a fixed point(focus) is equal to its perpendicular …

## Formulas for Conic Sections – Equations & Concepts

Here, you will learn general equation and formulas for conic sections and formula to distinguish between conic. Conic Sections A conic section, or conic is the locus of a point which moves in a plane so that its distance from a fixed point is in a constant ratio to its perpendicular distance from a fixed …

## Equation of Normal to Parabola in all Forms

The equation of normal to parabola in point form, slope form and parametric form are given below with examples. Equation of Normal to Parabola $$y^2 = 4ax$$ (a) Point form : The equation of normal to the given parabola at its point ($$x_1, y_1$$) is y – $$y_1$$ = $$-y_1\over 2a$$(x – $$x_1$$) Example : …

## Equation of Tangent to Parabola in all Forms

The equation of tangent to parabola in point form, slope form and parametric form are given below with examples. Condition of Tangency for Parabola : (a)  The line y = mx + c meets the parabola $$y^2$$ = 4ax in two points real, coincident or imaginary according as a >=< cm $$\implies$$ condition of tangency …

## Graph of a Parabola – Types of Parabolas

A parabola is locus of a point which moves in a plane, such that its distance from a fixed point called focus is equal to its perpendicular distance from a fixed straight line called directrix. Graph of a Parabola and their types are shown below. Basic Concepts of a Parabola (a) Focal distance : The …