The Ellipse. a b b a 3 4 When the size of a becomes the same as b, we get a circle.

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Presentation transcript:

The Ellipse

a b

b a

3 4

When the size of a becomes the same as b, we get a circle.

Definition: is the locus of all points which meet the condition... sum of distances to each focus is constant

c is the focus Relation to the focus:

a b c a

Sketch the following graphs

Write the equation of this ellipse.

Parametric equations of the ellipse Eliminate to obtain the equation of the ellipse

Parameter

Write down the parametric equations for these ellipses

Find the equation of the tangent to the ellipse at the point where

A line tangent to an ellipse at a point P makes equal angles with the lines through P and the foci.

It follows that a ray of light emanating from one focus of an ellipse will be reflected through the other focus.

A point moves so that the sum of its distances from the two points (1, 1) and (3, 1) is always 10. Find the equation of the locus of the point.

Homework  Exercises 13.5, 13.6  Delta Exercise 14.1  Number 7 onwards