This topic is about learning the graphs, equations and properties of the circle, ellipse, hyperbola and parabola, including directrix, focus and eccentricity on each conic session. Then, applying the features of each conic session to model situations accordingly.
Objectives:
1 Apply the geometry of conic sections in solving problems involves:
· selecting and using methods
· demonstrating knowledge of concepts and terms
· communicating using appropriate representations.
Relational thinking involves one or more of:
· selecting and carrying out a logical sequence of steps
· connecting different concepts or representations
· demonstrating understanding of concepts
· forming and using a model;
and also relating findings to a context, or communicating thinking using appropriate mathematical statements.
Let F and G be foci. For any point P on the Ellipse, the sum of the distances between the point and the two foci is always constant. (See Left Image)
It also happens that for an Ellipse, that constant sum (PF + PG) is also the length of the Major Axis.
How do "a" and "b" affect the shape of the graph?
Use desmos to investigate on it.
The new vertices are at (a+d, 0+e) or (-a+d, 0+e)
Practice Tasks