Describe the method for drawing an ellipse and explain foci of ellipse, midpoint, semi major axis.
Describe the method for drawing an ellipse and explain foci of ellipse, midpoint, semi major axis.
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.
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