It is known that the equation of parabola C is Y & # 178; - 2px-2ysin & # 178; the fourth power of θ + sin θ + 2pcos θ = 0 (1) find the coordinates of focus F of parabola C (2) make a straight line L with an inclination angle of 45 ° through F and intersect the parabola C at two points ab. when θ changes, calculate the abscissa range of the intersection of the middle vertical line of the chord AB and the X axis

It is known that the equation of parabola C is Y & # 178; - 2px-2ysin & # 178; the fourth power of θ + sin θ + 2pcos θ = 0 (1) find the coordinates of focus F of parabola C (2) make a straight line L with an inclination angle of 45 ° through F and intersect the parabola C at two points ab. when θ changes, calculate the abscissa range of the intersection of the middle vertical line of the chord AB and the X axis

The parametric equation of x = 2 / 1 + T & # 178;, y = 2T / 1 + T & # 178

x²+y²=4(1+t²)/(1+t²)²=4/(1+t²)=2x
We get: (x-1) &# 178; + Y & # 178; = 1
If expressed by the parametric equation of a circle:
x=1+cosθ
y=sinθ

Parametric equations of circle, ellipse, hyperbola and straight line

Circle x = a + RCOs θ, y = B + rsin θ
Ellipse: x = ACOS θ, y = bsin θ
Hyperbola: x = ASEC θ, y = btan θ

The equation of linear motion is s = s (T) = 3T & # 178; - 5T
(1) Find the average velocity of the object in 2 seconds to 4 seconds;
(2) Calculate the instantaneous velocity of the object in 2 seconds;
(3) Find the instantaneous velocity of the object at t0 second

By comparing the displacement formula of uniform velocity change motion, s = v0t + 0.5at ^ 2, we can see that the motion is uniform velocity change motion, V0 = - 5m / s, a = 6m / S ^ 2
The average velocity of 2s-4s is the instantaneous velocity calculated at the intermediate time 3, v = V0 + at = - 5 + 6 * 3 = 13m / s
The instantaneous velocity of 2S is v = V0 + at = - 5 + 6 * 2 = 7m / s
When t = 0, the velocity is the initial velocity - 5m / s