Before we embark on solving the problem, let us first explore the definition of ellipse.

[pic]
An ellipse is a curve that is the locus of all points in the plane the sum of whose distances [pic] and [pic] from two fixed points [pic] and [pic] (the foci) separated by a distance of [pic] is a given positive constant [pic]

[pic]
While [pic] is called the major axis, [pic] is the semi major axis, which is exactly half the distance across the ellipse. Similarly, the corresponding parameter [pic] is known as the semi minor axis.

Parallels drawn from the formula for the area of circle ([pic]) and formula for the area of an ellipse (A = [pic]ab)

Formula for the area of a circle:[pic] where [pic] is the area, and [pic] is the radius. In the case of a circle, radius a represents the semi major axis while radius b represents the semi minor axis. One can thus find the area of the circle through the formula A = [pic]ab, where a is equal to b. Hence circle, in actual fact, is a unique case of ellipse.

Proving that the area of an ellipse is πab

Procedures to take (Theory)

1. We have to let an ellipse lie along the x-axis and find the equation of the ellipse curve. 2. Upon finding the equation of the ellipse curve, we have to change the subject of the equation to y. (otherwise, we will have to do integration with respect to y if the subject of the equation is x.) 3. Next, applying what we have learnt, we can find the area bounded by the ellipse curve through definite integration between the 2 limits.

Calculations (Practical)
(Working steps are adapted from http://mathworld.wolfram.com/Ellipse.html)

Let an ellipse lie along the x-axis and find the equation of the figure where [pic]and [pic]are at [pic]and [pic]. a) Form an equation.
[pic]
b) Bring the second term to the right side and square both sides. [pic]
c)...

...Conics are surprisingly easy! There are four types of conic sections, circles, parabolas, ellipses, and hyperbolas. The first type of conic, and easiest to spot and solve, is the circle. The standard form for the circle is (x-h)^2 + (y-k)^2 = r^2. The x-axis and y-axis radius are the same, which makes sense because it is a circle, and from
In order to graph an ellipse in standard form, the center is first plotted (the (h, k)). Then, the x-radius is plotted on both...

...formed by the intersection of a cone by a plane which cuts obliquely the axis and the opposite sides of the cone. The ellipse is a conic which does not extend to infinity, and whose intersections with the line at infinity are imaginary. Every ellipse has a center, which is a point such that it bisects every chord passing through it. Such chords are called diameters of the ellipse. A pair of conjugate diameters bisect, each of them, all chords parallel...

...Chapter 13_Graphing the Conic Sections
Ellipses
In this study guide we will focus on graphing ellipses but be sure to read and understand
the definition in your text.
Equation of an Ellipse (standard form)
Area of an Ellipse
( x − h) 2 ( y − k ) 2
+
=1
a2
b2
with a horizontal axis that measures 2a units, vertical axis
measures 2b units, and (h, k) is the center.
The long axis of an...

...Section
Question 1.
a) What number must be subtracted from 2x3 – 5x2 + 5x so that the resulting polynomial has a factor 2x – 3 ? [3]
b) D, E, F are mid points of the sides BC, CA and AB respectively of a Δ ABC. Find the ratio of the areas of Δ DEF and Δ ABC. [3]
c) A man borrowed a sum of money and agrees to pay off by paying Rs 3150 at the end of the first year and Rs 4410 at the end of the second year. If the rate of compound interest is 5%...

...Surface Area Formulas
In general, the surface area is the sum of all the areas of all the shapes that cover the surface of the object.
Cube | Rectangular Prism | Prism | Sphere | Cylinder | Units
Note: "ab" means "a" multiplied by "b". "a2" means "a squared", which is the same as "a" times "a".
Be careful!! Units count. Use the same units for all measurements. Examples
|Surface Area of a Cube = 6 a 2...

...Explain each of the areas of learning and development and how these are interdependent.
Personal social and emotional has three aspects, making relationships, managing feelings and behaviour and self-confidence and self-awareness. This area is all about the child’s relationships with other people and themselves. Children need to develop relationship with the people around the for example the children they play with and come into contact with. The staff that work...

... = 3(5) – 3
= 12 m
(6.03)
61) What is the area of a square that has a side length of:
a) 9 units
b) 11 units
Area of a square: = (Side length)2
a) A = (9)2 b) A = (11)2
= 81 u2 = 121 u2
62) A rectangle has a length of 8 in and a width of 5 in. Find the area.
Area of a rectangle: = (L)(W)
A...

...special needs -feel secure, comfortable and a place where they belong.
The interest areas should allow the children choices to explore, make things, experiment, and pursue their interests. The choices should include"quiet zone" areas for reading, art activities, and games. Areas should also be set for block building, dramatic play, woodwork, sand and water (discovery table) for active engagements.
All the interest areas should...