An ellipse is a geometric figure in the plane that is given by the formula x? / A? + Y? / B? = 1 To construct an ellipse with the help of a compass and a ruler, it is necessary to construct points belonging to it.
We introduce definitions related to the concept of an ellipse.
Two points F1 and F2 are called the foci of an ellipse, if for any point M taken on an ellipse, the sum of the distances F1M + F2M is a constant value.
The segment AB passing through the foci whose ends lie on an ellipse is called the semimajor axis.
A segment of CD perpendicular to the segment AB and passing through its middle is called the semimajor axis.
Let the lengths of the axes of the ellipse AB and CD be given. To build an ellipse, you can use the following algorithm.
Draw two perpendicular lines and from the point of intersection we plot the segments horizontally equal to AB / 2 and vertically equal to CD / 2
Draw two circles with radii AB / 2 and CD / 2. From the center of the circle draw a few rays.
Through the points of intersection of the constructed rays with the circles we draw the segments parallel to the axes of the ellipse.
We select the intersection points of the constructed segments, these are the points belonging to the ellipse.
By joining the obtained points, we obtain an ellipse.