Through the focus F of the parabola y ^ 2 = 4x, make a straight line intersection parabola with an inclination angle of θ, and use θ to represent the length of AB at two points ab

Let a (x1, Y1), B (X2, Y2) use the definition of parabola, then | AF | = X1 + 1, | BF | = x2 + 1 | | ab | = X1 + x2 + 2 straight line is y = Tan θ (x-1) substituted into the parabola equation, then Tan |; 178; θ (x-1) # 178; = 4x is tan | | 178; θ x # 178; - (2tan |; 178; θ + 4

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1. The parabolic standard equation with chord length of 16, which is perpendicular to the x-axis and has the focal point, is solved
2. (y ^ 3-4x ^ 2) / (x ^ 3 + 2Y) = 44 / 31 given DX / dt = 5 x = - 3 y = - 2 find dy / DT
3. Solve DX / (x + T) = dy / (- y + T) = DT
4. Given y = x times LNX, find dy=___ DX? Please write the standard steps and the final answer,
5. Find the integral of ∫ DX / X (X & # 178; + 1)?
6. Let f (x) be differentiable on the interval [0,1], f (0) = 0,0
7. Let f (x) be continuous on the interval [a, b], and prove that 1 / (B-A) ∫ f (x) DX ≤ (1 / (B-A) ∫ F & # 178; (x) DX) ^ & # 189;
8. Let f (x) be continuous on the interval [a, b], then the value of ∫ f (x) DX - ∫ f (T) DT (the interval is [a, b]) is?
9. Let f (x) be continuous on (0, π / 2) (closed interval), f (x) = xcosx + ∫ f (T) DT, then ∫ f (x) DX has upper limit and lower limit π / 2 The upper limit is flat π / 2 and the lower limit is 0
10. Let the variable upper limit integral ∫ (0, x) f (T ^ 2) DT = x ^ 3, then 2 ∫ (0,1) DX =? Sorry, wrong number. If the variable upper limit integral ∫ (0, x) f (T ^ 2) DT = x ^ 3, then 2 ∫ (0,1) f (x) DX =?
11. Given that the inclination angle of the line passing through the focus of the parabola y ^ 2 = 4x is 60 degrees, then the distance from the vertex to the line is?
12. Given the parabola y & sup2; = 4x, make a straight line with an inclination angle of π / 4 through its focus F, intersect the parabola at two points a and B, let the vertex of the parabola be o, and find △ a Given the parabola y & # 178; = 4x, make a straight line through its focus f with an inclination angle of π / 4, intersect the parabola at two points a and B, let the vertex of the parabola be o, and calculate the area of △ ABC
13. Make a straight line with a slope of 45 degrees through the focus f with the square of parabola y = 4x, intersect the parabola at two points a and B, and find the distance from the midpoint C of AB to the parabola collimator
14. Through the focus F of parabola y2 = 4ax (a > 0), make two mutually perpendicular focus chords AB and CD, and find the minimum value of | ab | + | CD |
15. Given that the vertex is at the origin and the focus is on the Y-axis of the parabola C section line y = 2x-1, the chord length is 2 root sign 10, and the equation of parabola C is obtained
16. Write the standard equation of parabola according to the following conditions: (1) the focal point is f (0,3), (2) the distance from the focal point to the collimator is 2
17. In a parabola, the distance from the focus to the collimator is 4, and the focus is on the y-axis. Write out the standard equation of the parabola and find the solution
18. Find the standard equation of a parabola satisfying the following conditions. On the parabola y ^ 2 = 24ax (a > 0), there is a point m whose abscissa is 3 and its distance from the focus is 5
19. Translate the square of the parabola y = 2x left and right so that it intersects the X axis at point a and the Y axis at point B. if the area of △ AOB is 8, find the analytical formula of the parabola after translation
20. Parabola y = 2x ^ 2 + 1 and parabola y = - 2x ^ 2 + k are at most the same_____ Intersection points