1, range: pay attention to the difference and connection between equation and function; The maximum value related to ellipse is the range of variables; Draw an ellipse.
2. Symmetry: the center of ellipse and its symmetry; The basis for judging the symmetry of curve about X axis, Y axis and origin; If a curve has any two symmetries about the X-axis, Y-axis and origin, then it also has another symmetry. Pay attention to the inherent property that the ellipse does not change with the coordinate axis.
3. Vertex: the vertex coordinates of the ellipse; The vertex of a general conic curve is the intersection of the curve and the axis of symmetry; The geometric meaning of a, b and c in an ellipse (the characteristic triangle of the ellipse and the trigonometric function representation of eccentricity).
4. Centrifugal rate: the definition of centrifugal rate; Range of eccentricity of ellipse: (0,1); The influence of the change of ellipse eccentricity on ellipse: when E tends to 1, C tends to A, at this time, the ellipse is flatter; When e tends to 0: c tends to 0, the ellipse is closer to the circle; If and only if a=b and c=0, the two focal points coincide and the ellipse becomes a circle.
Investigation and study on the deformation of textbook examples;
1, the concepts of perihelion and apohelion: the maximum value of the distance from any point P(x, y) on the ellipse to the focus of the ellipse: a+c and the minimum value: a-c, and the coordinates of the point with the maximum value;
2. The second definition of ellipse and its application: the directrix equation of ellipse, the distance between two directrix, focal length: focal length formula.
3. Given a point M on the ellipse, find a point P on the ellipse to minimize the sum of the distances from the point P to the point M and the ellipse directrix.
4. Parametric equation of ellipse and eccentric angle of ellipse-Simple application of elliptic parametric equation;
5. The positional relationship between the straight line and the ellipse, the chord length and the midpoint of the chord when the straight line intersects the ellipse.
An ellipse is a curve around two focal points on a plane, so for each point on the curve, the sum of the distances to the two focal points is constant. Therefore, it is a generalization of a circle, and it is a special type of ellipse with two focuses at the same position. The shape of an ellipse (how to "stretch") is expressed by its eccentricity, which can be any number from 0 (the limit case of a circle) to close to but less than 1.
The standard equation of ellipse * * * is divided into two cases [1]:
When the focus is on the X axis, the standard equation of the ellipse is: X 2/A 2+Y 2/B 2 =1,(a>b>0);
When the focus is on the Y axis, the standard equation of the ellipse is: Y 2/A 2+X 2/B 2 =1,(a>b>0);
Where a 2-c 2 = b 2.
Deduction: pf1+pf2 >; F 1F2(P is the point f on the ellipse as the focus)
I hope this helps.