Graphing Conic Sections

Introduction to graphing conic sections:

There are usually four conic sections available :

Circle
Parabola
Ellipse
Hyperbola
In this article we deal with graphing of different conic sections . Graphing means plotting of the given conic on to a graph paper depending on the nature of the given conic section .

Graphing of the conic sections usually starts with identifying the center of the conic section then also the basic parameters like axis of symmetry , radius , focus, vertices etc. Then it will be easier to graph.

Here are some examples given :

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Graphing Conic Sections : Solved Examples

Example 1 : Draw the graph of the given parabola

y=`(x-4)^(2)` +1

Solution : For this parabola ,

The vertex is the point (4,1)
The axis of symmetry is the line x=4.
The directrix is the line y=0.75
We have to first find the points of the given function equation and then we plot the graph that is we have to plug in different values of x in the equation .

By putting x = 2 , we get y = 5

Also by putting x = 6 , we get y = 4 + 1 that is y = 5

Graph :

Example 2 : Draw the graph of the given circle

`x^(2)` + `y^(2)` = 16

Solution : Centre of the given circle is ( 0,0 )

Radius is equal to 4

Through the centre coordinate , we have to add the value of radius to the coordinates and get the four plotting points as shown in the graph .

Graph :

Graphing Conic Sections : Practice Problems

Problem 1 : Draw the graph of the given parabola

y=2`(x-4)^(2)` +5

Problem 2 : Draw the graph of the given circle

`x^(2)` + `y^(2)` = 25

Problem 3 : Draw the graph of the given parabola

y=3`(x-7)^(2)` +4