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Describe the method for drawing an ellipse and explain foci of ellipse, midpoint, semi major axis.
Solution
Select two points $\mathrm{F}_{1}$ and $\mathrm{F}_{2}$.
A string has its ends fixed at $\mathrm{F}_{1}$ and $\mathrm{F}_{2}$.
With the tip of a pencil stretch the string taut and then draw a curve by moving the pencil keeping the string taut throughout.
The closed curve you get is called an ellipse.
For any point $\mathrm{T}$ on the ellipse, the sum of distances from $\mathrm{F}_{1}$ and $\mathrm{F}_{2}$ is a constant. $\mathrm{F}_{1}$ and $\mathrm{F}_{2}$ are called the foci.
Join the points $\mathrm{F}_{1}$ and $\mathrm{F}_{2}$ and extend the line to intersect the ellipse at points $\mathrm{P}$ and $\mathrm{A}$ as shown in figure. The midpoint of the line $PA $is the centre of the ellipse $"O"$.
The length $\mathrm{PO}=\mathrm{AO}$ is called the semi major axis of the ellipse.
