Directrices and Eccentricity

Directrices and eccentricity are terms commonly used in geometry to describe the properties of a conic section, which is a curve obtained by the intersection of a plane with a cone. These terms are particularly useful in understanding the properties of ellipses and hyperbolas. The directrices of an ellipse are two lines that are equidistant…

Shift of origin

Shifting the origin in analytical geometry involves moving the coordinate system to a new location. This can be done by adding or subtracting a constant value from each coordinate. Suppose the original coordinate system has an origin at point O(0,0). To shift the origin to a new point P(a,b), we can use the following transformation:…