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What is the second definition of ellipse, hyperbola and parabola?
Ellipse: when the ratio of the distance between point m and a fixed point and its distance to a fixed line is constant E = C / a (0e1), the trajectory of this point is an ellipse, the fixed point is the focus of the ellipse, the fixed line is called the quasi line of the ellipse, and the constant e is the eccentricity of the ellipse.: hyperbola: when the distance between point m and a fixed point and its distance to a fixed line
What is the second definition of ellipse? Hyperbola, parabola also apply?
A set of points on a plane where the ratio of the distance to a fixed point to the distance to a fixed line is constant
The fixed point is the focus, the fixed line is the guide line on the same side as the focus, and the ratio is the eccentricity
Focal radius formula of parabola
When the parabolic equation is y ^ 2 = 2px (P > 0) (opening to the right),
Focal radius r = x + P / 2 (where x is the abscissa on the parabola and P is the focal distance) (calculated by using the second definition of parabola)
When the opening direction of the parabola is the other three directions, the same principle can be obtained by using the second definition of the parabola. If the focus is not on the coordinate axis, just translate x accordingly, and P remains unchanged
What is the hyperbolic path length formula
2B / a the ellipse is also a parabola and 2p
The difference and relation of ellipse, hyperbola and parabola
Circle, ellipse, hyperbola and parabola belong to conic curves. As early as 2000 years ago, ancient Greek mathematicians were very familiar with them. Ancient Greek mathematician aporoni used the method of plane cutting cone to study these curves. Cut the cone with a plane perpendicular to the cone axis to get a circle; Tilt the plane gradually to get
Among the chords passing through the focus on the conical curve (parabola, ellipse, hyperbola), the path is the shortest,
Yes, it's called drift
Its length is 2ep
Where e is the eccentricity,
P is the focal collimation distance, that is, the distance from the focus to the collimation line
I wish you a happy study!
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