Definition of Ellipse and Circle
Ellipse
The locus of a point in a plane whose distance from a fixed point bears a constant ratio, less than one to its distance from a fixed line is called ellipse. An ellipse is the set of all points (x, y) in the plane such that the sum of the distances from (x, y) to two fixed points is some constant. The two fixed points are called the foci, which is the plural of focus.
Circle
A circle is the locus of a point which moves in such a way that its distance from a fixed point is always constant. The fixed point is called the centre of the circle and the constant distance is called the radius of the circle.
Geometric Construction
The geometric construction of an ellipse can easily be accomplished with some very simple tools: a piece of string, a pencil, two pins, and a piece of paper. Simply stick the two pieces of string into the piece of paper using the two pins. Pull the string tight (using the pencil) until a triangle is built with the pencil and the two pins as vertices. Now, keeping the string pulled tight, move the pencil around until the ellipse is traced out.
Example: Consider the equation Given our comments above, this equation yields an ellipse. We see that and and the graph of this ellipse is the following:
Consider the equation
Given our comments above, this equation yields an ellipse. We see that
a=5
and
b=3
and the graph of this ellipse is the following:
Ellipse
The locus of a point in a plane whose distance from a fixed point bears a constant ratio, less than one to its distance from a fixed line is called ellipse. An ellipse is the set of all points (x, y) in the plane such that the sum of the distances from (x, y) to two fixed points is some constant. The two fixed points are called the foci, which is the plural of focus.
Circle
A circle is the locus of a point which moves in such a way that its distance from a fixed point is always constant. The fixed point is called the centre of the circle and the constant distance is called the radius of the circle.
Geometric Construction
The geometric construction of an ellipse can easily be accomplished with some very simple tools: a piece of string, a pencil, two pins, and a piece of paper. Simply stick the two pieces of string into the piece of paper using the two pins. Pull the string tight (using the pencil) until a triangle is built with the pencil and the two pins as vertices. Now, keeping the string pulled tight, move the pencil around until the ellipse is traced out.
Example: Consider the equation Given our comments above, this equation yields an ellipse. We see that and and the graph of this ellipse is the following:
Consider the equation
Given our comments above, this equation yields an ellipse. We see that
a=5
and
b=3
and the graph of this ellipse is the following:
