THE FOCI (FOCUS) OF AN ELLIPSE AND TANGENTS

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THE FOCI (FOCUS) OF AN ELLIPSE AND TANGENTS

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The FOCI (focus) of an ellipse play an important role. The position of the foci, determine the eccentricity of the ellipse. In simple terms, the position of the foci determines how much the ellipse deviates from a true circle shape.

To find the FOCI, set a compass to half the distance of the major axis. Place the compass point at the top of the ellipse (co-vertex)and strike an arc on either side of the major axis (as shown below).

The two foci are situated on the major axis. The distance from any single point on the ellipse to both foci is the same. See the three lines drawn on the ellipse below.

DRAWING A TANGENT TO ANY GIVEN POINT ON AN ELLIPSE

A tangent is a line that touches a curve at a point, but does not intersect with it. There is a specific technique when drawing a tangent to a point on a curve. Tangents are very important in Mathematics, Geometrical Drawing and Engineering.

HOW TO DRAW A TANGENT THROUGH A POINT ON AN ELLIPSE

STAGE ONE

STAGE TWO

STAGE THREE

STAGE FOUR

STAGE FIVE

STAGE SIX

STAGE SEVEN

STAGE EIGHT

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