GUIDE TO UNDERSTANDING PARABOLAS
Why is a Parabola called a Conic?
You will first learn how Parabolas originated from Conics and the difference between a Parabola, Ellipse and Hyperbola.
A Parabola is the set of all points in a plane equidistant from a fixed point and a fixed line. The fixed point is called the focus and the fixed line is called the directrix. Problems on these are illustrated below.
Basic types of Parabolas and how to remember them.
Next, you will learn the 4 basic types of Parabolas. Left, Right, Top and Bottom, as I tell my students. You will learn how to calculate the equation of the axis, the directrix and the focus for each type. The following image illustrates what you need to remember for the 1st form.
You'll learn how to solve problems on all these forms in this course.
What happens when the vertex is not the origin?
What you need to do is to complete the square of the 2nd degree term and you will get the vertex as (x - h, y - k). In this case, you need to remember that the x axis is shifted h units to the right and the y axis is shifted k units on top.
On the other hand, if the vertex is (x + h, y + k), the x axis is shifted h units towards the left and the y axis is shifted k units downwards. You'll need to use this while doing curve sketching in Integration.
HOW TO FIND THE EQUATION OF A PARABOLA FROM ITS FOCUS AND DIRECTRIX
How do you find the equation of a parabola given its focus and directrix. Watch this video to find out. Here, we learn how a parabola is derived when a plane cuts a cone. We learn that, for a parabola, distance of a point from the focus = distance of the point from the directrix. We solve problems based on this principle and also learn how to calculate equation of the axis and the coordinates of the vertex. Problems of the type-" Find the equation of a parabola with focus at (3,-4) and directrix x + y = -4 . Also find the equation of the axis " are discussed and more such problems. Online tutoring is provided. You can choose between specific topics or the entire course. For more details, you can contact me on firstname.lastname@example.org.
TYPES OF PARABOLAS
This presentation explains the 4 basic types of parabolas. It also shows how the focus, vertex, equation of the axis and directrix can be determined in each case. It also explains how the values change when the origin is shifted A number of problems are solved and illustrated.You will learn how to calculate the vertex, focus, equation of the directrix and length of the latus rectum for these parabolas. Online classes are provided. You can choose between a specific topic or the entire course. For more details, you can contact me on email@example.com
CONDITION OF TANGENCY FOR A PARABOLA
You will learn how to calculate the tangent to a parabola in this video. You will also learn how to find the point of contact and check the condition of tangency. A useful video with a lot of solved problems is provided. Online classes are also available. You could choose a specific topic or the entire course. For more details, you can contact me on firstname.lastname@example.org.