If the hyperbola X29 − y2 = 1 has moving points P, F1 and F2, then the trajectory equation of the center of gravity m of △ pf1f2 is______ ．

A = 3, B = 1, C = 10, F1 (- 10, 0), F2 (10, 0) can be obtained from hyperbolic equation. Set point P (m, n), then & nbsp; m29 − N2 = 1. Let g (x, y) be the center of gravity of △ pf1f2, then x = m + 10 − 103, y = n + 0 + 03 can be obtained from the coordinate formula of the center of gravity of triangle

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1. It is known that F 1 and F 2 are the left and right focal points of the ellipse C: x 24 + y 23 = 1 respectively, and P is the moving point on the ellipse C, then the trajectory equation of the center of gravity g of △ pf1f 2 is () A. x236+y227＝1(y≠0)B. 4x29+y2＝1(y≠0)C. 9x24+3y2＝1(y≠0)D. x2+4y23＝1(y≠0)
2. There is a moving point P on the ellipse X / 9 + y2 = 1. F1 and F2 are the two focal points of the ellipse. The trajectory equation of the center of gravity m of △ pf1f2 is obtained
3. If the hyperbola X29 − y2 = 1 has moving points P, F1 and F2, then the trajectory equation of the center of gravity m of △ pf1f2 is______ ．
4. Let AB be the chord passing through the center of the ellipse and f be a focal point of the ellipse? The ellipse is x ^ 2 + 2Y ^ 2 = 1
5. It is known that the eccentricity of ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a is greater than B is greater than 0) is root sign 2 / 2, and its left and right focuses are F1F2 respectively. P is a point on the ellipse. Vector Pf1 × vector PF2 = 3 / 4, absolute value of OP = root sign 7 / 2 1. Solving the equation of ellipse C 2. The moving line L passing through point s (0, - 1 / 3) intersects with ellipse C and a, B. question: is there a fixed point m on the y-axis so that a circle with diameter AB passes through point m? If there is, find out the coordinates of M. if not, explain the reason
6. The focal length of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 is 2C. If the three numbers a, B and C form an equal ratio sequence in turn, calculate the eccentricity E
7. If the point P (C, 2C) is in the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0), then the eccentricity of the ellipse E= Such as the title
8. If the projection of the two intersection points of the straight line y = 22x and the ellipse x2a2 + y2b2 = 1, a > b > 0 on the X axis is exactly the two focal points of the ellipse, then the eccentricity e of the ellipse is equal to () A. 32B. 22C. 33D. 12
9. If the half focal length of the ellipse x ^ 2 / A ^ 2 + y ^ / b ^ 3 = 1, (a > b > 0) is C, and the abscissa of the straight line y = 2x and a focus of the ellipse is exactly C, then the eccentricity of the ellipse
10. How to determine the focus of the ellipse Some answer questions, Taking the long and short axis of the ellipse as the center and the short axis as the diameter, draw a circle, and the intersection of the long axis of symmetry is the focus of the ellipse.
11. If F1 and F2 are the focus of the ellipse x ^ 2 / 25 + y ^ 2 / 16 = 1, and P is the point on the ellipse that is not on the X axis, then the trajectory equation of the center of gravity g of △ pf1f2 is
12. Ellipse x ^ 2 / A ^ 2 + y ^ 2 = 1, triangle ABC takes a (0,1) as the right vertex, B, C on the ellipse, the maximum area of triangle is 27 / 8, find the value of A
13. Let the center of the ellipse C be at the origin, the focus on the Y axis, and the eccentricity be 2 / 2 of the root sign 1. Find the standard equation of ellipse C 2. If the line L with slope 2 passes through the focus of ellipse C on the positive half axis of Y axis and intersects with the ellipse at two points AB, then | AB is obtained|
14. It is known that the left and right focal points of the ellipse x ^ 2 / 2 + y ^ 2 / 1 = 1 are F1 and F2 respectively. If the straight line passing through point P (0, - 2) and F1 intersects the ellipse at two points a and B, find the triangle ABF It is known that the left and right focal points of the ellipse x ^ 2 / 2 + y ^ 2 / 1 = 1 are F1 and F2 respectively. If the straight line passing through point P (0, - 2) and F1 intersects the ellipse at two points a and B, the area of triangle abf2 is calculated
15. Let a straight line passing through the left focus F1 of the ellipse x ^ 2 / 4 + y ^ 2 / 3 = 1 and with an inclination angle of 45 degrees intersect the ellipse and find the perimeter of the triangle abf2 at two points ab
16. If the center of the ellipse x ^ 2 / 25 + y ^ 2 / 16 = 1 is a straight line and intersects with the ellipse at two points a and B, and F1 is the focus of the ellipse, then the maximum area of the triangle f1ab is
17. Let point F1 be the left focus of x ^ 2 / 3 + y ^ 2 / 2 = 1, and the right focus of the chord AB passing through the ellipse. Find the maximum area of triangle f1ab. Remember to find the maximum!
18. Let a be a moving point on the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1, and the chords AB and AC pass through the focus F1 and F2 respectively. When AC is perpendicular to the X axis, there is exactly | AF1 |: | af2 | = 3:1, (1) find the eccentricity of the ellipse (2) Let AF1 = mf1b, af2 = nf2c, and prove that M + n is the fixed value 6 (all letters are vectors)
19. If AB is the chord passing through the center of the ellipse X & # 178 / 25 + Y & # 178 / 16 and F1 is the left focus, then the maximum area of △ Abf1 is___ 12___ ,
20. Let p be a point on the ellipse x ^ 2 / 5 + y ^ 2 / 25 = 1, and F1 and F2 be the two focuses of the ellipse. If Pf1 ⊥ PF2, then the absolute value of the difference between Pf1 and PF2 A.0 B.2√5 C.4√5 D.2√15