What are the properties of ellipse?

Property 1: Tangents drawn from a common point, outside the curve are equally inclined to the focal points. PROPERTY 2 A circle containing the foci and a point p on the curve will intersect the minor axis at the points of intersection of the tangent and the normal to the curve from point p. PROPERTY 3 The length of the minor axis of an ellipse can be found by constructing a line perpendicular to the axis from the focal points, where this line intersects the auxiliary circle will give the length of the minor axis. PROPERTY 4 Conjugate Diameters Any diameter of the ellipse, as shown here, may be referred to as a conjugate diameter. This example shows the short conjugate diameter, the long conjugate diameter would pass through the centre and be parallel to a tangent to the curve at r and s. Constructing the Ellipse given the Conjugate Diameter PROCEDURE 1. Construct the conjugate diameters TU (long) and RS (short). 2. Take a line from R perpendicular to TU of length CU to find point D. 3. Join D to C. 4. Construct a circle of diameter DC. 5. Take a line from R through the centre of the circle and project it on to meet the circle at G. 6. A line from G through C will give the direction of the minor axis. 7. RE = 1/2 the minor axis. 8. A line from E through C will give the direction of the major axis. 9. RG = 1/2 the major axis. 10. You now have the major and minor axis and can construct the curve. NOTE: The curve passes through points R, S, T and U. PROPERTY 1 Tangents drawn from a common point, outside the curve are equally inclined to the focal points. PROPERTY 2 A circle containing the foci and a point p on the curve will intersect the minor axis at the points of intersection of the tangent and the normal to the curve from point p. PROPERTY 3 The length of the minor axis of an ellipse can be found by constructing a line perpendicular to the axis from the focal points, where this line intersects the auxiliary circle will give the length of the minor axis. PROPERTY 4 Conjugate Diameters Any diameter of the ellipse, as shown here, may be referred to as a conjugate diameter. This example shows the short conjugate diameter, the long conjugate diameter would pass through the centre and be parallel to a tangent to the curve at r and s. Constructing the Ellipse given the Conjugate Diameter PROCEDURE 1. Construct the conjugate diameters TU (long) and RS (short). 2. Take a line from R perpendicular to TU of length CU to find point D. 3. Join D to C. 4. Construct a circle of diameter DC. 5. Take a line from R through the centre of the circle and project it on to meet the circle at G. 6. A line from G through C will give the direction of the minor axis. 7. RE = 1/2 the minor axis. 8. A line from E through C will give the direction of the major axis. 9. RG = 1/2 the major axis. 10. You now have the major and minor axis and can construct the curve. NOTE: The curve passes through points R, S, T and U. read less