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!

Please draw a picture, then F1F2 = 1
Look at the triangle af1f2 and bf1f2
Just compare the distance between a, B and X axis
So obviously, when AB is perpendicular to x, the area has a maximum
→S=8√3/3

RELATED INFORMATIONS

1. 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
2. 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
3. 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
4. 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|
5. 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
6. 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
7. 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______ ．
8. 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)
9. 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
10. 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______ ．
11. 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)
12. 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___ ,
13. 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
14. The focus F1, F2 and point P of the ellipse x ^ 2 / 9 + y ^ 2 / 2 = 1 are on the ellipse. If the absolute value of Pf1 = 2 ~ then the absolute value of PF2 = angle f1pf2, the size of PF2 is
15. If P is on the ellipse, and (absolute value of Pf1) - (P It is known that the two focal points of ellipse are F1 (0, - 1) F2 (0,1) eccentricity e = 1 / 2 Find 1. Elliptic equation 2. If P is on the ellipse and (absolute value of Pf1) - (absolute value of PF2) = 1, find the cos angle f1pf2
16. Given that P is any point on the ellipse x ^ 2 / 4 + y ^ 2 = 1, F1 and F2 are the two focuses of the ellipse, find the minimum value of absolute value Pf1 ^ 2 + absolute value PF2 ^ 2
17. If AB is the chord passing through the center of the ellipse x2 / A + Y2 / B2 = 1 and F1 (C, 0) is the focus of the ellipse, then the area of the triangle f1ab is the maximum
18. If AB is the chord passing through the center of the ellipse x2 / 25 + Y2 / 16 = 1 and F1 is the focus of the ellipse, then the area of the triangle f1ab is the largest Method 2 (basic method): s △ f1ab = s △ oaf1 + s △ obf1 = (C × y1-y2) × 2 = (3 × y1-y2) × 2 Case (1): when k exists, let AB: y = KX be substituted into the ellipse x2 / 25 + Y2 / 16 to find y1-y2, and get 60 × √ K square × √ [25 × K square × 16] / (25 × K square × 16) ＜ 12 Case (2): when K does not exist, s = B × 2C △ 2 = 12 According to (1) (2), s ≤ 12 My formula is 60 ×√ K square × √ [25 × K square + 16] / (25 × K square + 16), then I get 15,
19. Let AB be the chord of the center of the ellipse x ^ 2 / 9 + y ^ 2 / 25 = 1, and f be a focal point of the ellipse, then the maximum area of the triangle ABF is
20. Through the focus F of the ellipse x ^ 2 / 4 + y ^ 2 = 1, make the chord AB, and find the maximum area of the triangle AOB (o is the coordinate origin) Ask for detailed explanation