Ellipse directrix formula is a mathematical expression to describe ellipse.
1. What is an ellipse?
Ellipse is a special closed curve on a plane, and its shape is similar to an elongated circle. An ellipse is defined by two focal points and a line segment connecting the focal points, and it has symmetry in the plane.
Second, the meaning of the elliptic directrix formula
The ellipse directrix formula describes the coordinates of each point on the ellipse. Through this formula, given the parameter θ, the position of the point on the ellipse can be calculated.
1, x=a*cosθ ":This formula represents the x coordinate of a point on an ellipse. A is the length of the long semi-axis of an ellipse, and cosθ represents the cosine of θ. Given the value of θ, the X coordinate of this point on the ellipse can be calculated.
2.y=b*sinθ ":This formula represents the y coordinate of a point on an ellipse. B is the length of the minor axis of the ellipse, and sinθ represents the sine value of θ. Given the value of θ, the Y coordinate of this point on the ellipse can be calculated.
Third, the image characteristics of elliptic directrix formula
Through the formula of ellipse directrix, the image characteristics of ellipse can be obtained.
1, coordinate origin: In the directrix formula, when θ equals 0, the coordinate of this point is (x, y)=(a, 0), which is the endpoint of the right half of the ellipse. When θ equals π, the coordinate of this point is (x, y)=(-a, 0), which is the endpoint of the left half of the ellipse.
2. Symmetry: Because the cosine function and sine function in the directrix formula are periodic functions, the ellipse figure has symmetry. That is to say, the ellipse is centered on the coordinate origin and symmetrical about the X axis and Y axis.
3. Long and short semi-axes: Parameters A and B in the directrix formula represent the long and short semi-axes of the ellipse respectively. The long semi-axis determines the transverse stretching degree of the ellipse, and the short semi-axis determines the longitudinal stretching degree of the ellipse.
4. directrix: The directrix of an ellipse is a straight line connecting two focal points. The θ parameter in the directrix formula can represent a point on the directrix.
Fourth, the application field
Elliptic directrix formula is widely used in mathematics and physics, such as orbital motion, optics and astronomy. Through the formula of ellipse directrix, we can describe and calculate the shape and position of ellipse under specific circumstances, and then analyze the problem and draw a conclusion.
Verb (abbreviation of verb) conclusion
Ellipse directrix formula is a mathematical expression to describe ellipse. Given the parameter θ, the coordinates of each point on the ellipse can be calculated. The directrix formula can reveal the characteristics and properties of elliptical images and has a wide range of applications.