How to determine the integral range of definite integral of polar coordinate equation? For example, ρ = 2A (2 + cos θ)

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1. 1.. P is a point on the ellipse x ^ 2 / 25 + y ^ 2 / 16 = 1, F1, F2 are the focus, if ∠ f1pf2 = 30 °, then the area of △ f1pf2 is________ 2. Given that P is the point on the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0), F1 and F2 are the two focal points on the left and right of the ellipse. If ∠ f1pf2 = 60 ° and the area of △ f1pf2 is [(radical 3) / 9] · a ^ 2, (1) calculate the eccentricity of the ellipse (2) If the line X - (radical 6) · y = 0 intersects the ellipse at two points a and B, and the vector F1A · vector F1B = - 1, the equation of the ellipse is obtained 3. The left and right focus of the ellipse x ^ / 9 + y ^ 2 / 5 = 1 are F1 and F2 respectively. Point a (1,1) is inside the ellipse and point P is on the ellipse. Find the maximum value of (1) | PF2 | - | PA | (2) find the minimum value of | PA | + | Pf1 |
2. Given the line L: y = 3x + 3, find the equation of (1) line L with respect to the symmetric line at point m (3,2)
3. I have forgotten the growth rate formula, the reduction rate formula, the area of a circle, the area of a sector and the arc length formula
4. What's the perimeter of a rectangle made of five squares a centimeter like this
5. The base circumference of fruit cone is 20 π, and the center angle of the fan-shaped circle is 120 ° after the lateral expansion
6. Given the function y = sin (cosx), then y '= ()
7. Finding the derivative of Ln (x + √ 1 + x square)
8. N-order derivative of y = ln (x-1 / x + 2)
9. Find the n-order derivative (n ≥ 3) of y = (x ^ 2) ln (1 + x) at x = 0
10. The derivative of F (x) = ln (x)
11. Let f (x) = - x square + 2aX + a square satisfy f (2) = f (a)
12. Using mathematical language to describe the process of roots of quadratic equation AX ^ 2 + BX + C = 0 A x^2+4x+3=0 B x^2-4x+3=0 C x^2+8x+9=0 D x^2-8x+9=0
13. It is known that the equation of hyperbola is X-Y / 3 = 1. A straight line passing through the right focus of hyperbola with a slope of K intersects hyperbola at two points a and B, and OA ⊥ ob is used to find K
14. The detailed process is needed to solve the ternary linear equations - A + B + C = - 22, C = - 8, 4A + 2B + C = 8
15. X + y = XY, x = 0, y = 0... X = 2, y = 2... We also need a set of
16. It is known that the value of X which makes the derivative of the function y = X3 + ax2-43a 0 also makes the value of y 0, then the value of constant a is () A. 0b. ± 3C. 0 or ± 3D
17. Blank space to answer 1. Change the quadratic function y = - 2x2 (quadratic) + 4x + 3 to y = a (x + m) 2 + K 2. Quadratic function y = X2 (quadratic) + X-5 when the minimum value of independent variable x =, y is 3. It is known that the image of the quadratic function y = (m-2) X2 (quadratic) + M2 (quadratic, not explained) - m-2 of X passes through the origin, then M =. At that time, y increases with the increase of X 4. For the image of y = 2 (x-3) 2 + 2, the following statement is correct () A. The mark of fixed point is (- 3,2) B. the axis of symmetry is y = 3 C. When x is greater than or equal to 3, y increases with the increase of X. when x is greater than or equal to 3, y decreases with the increase of X 5. In the same coordinate system, make the image of y = 2x2 + 2, y = - 2x2-1, y = half X2, then they () A. It's all about the y-axis symmetry B. the vertices are all at the origin C. they're all parabolas, opening up D. they're all wrong 6. It is known that the intersection of a parabola and x-axis is a (- 2,0), B (1,0), and passes through point C (2,8) (1) Find the analytic formula of the parabola. (2) find the vertex coordinates of the parabola
18. Given that the vector M = (3,4) the vector m-the absolute value of the vector n = 1, then the value range of the absolute value of the vector n
19. How to find the plane normal vector, please explain the specific method!
20. Set a = {(x, y) y = x & # 178; + MX + 2}, set B = {(x, y) X-Y + 1 = 0,0 ≤ x ≤ 2}, if a ∩ B ≠ & # 8709;, find the value range of real number K