![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > 1) a focus is F1, point P is on the ellipse, and / op / = / of 1 /, then the area of triangle opf1 Ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1, a focus is F1, point P is on the ellipse, and / op / = / of 1 /, then the area of triangle opf1 by Answer: 1 / 2 Newspapers 24-8
I think your answer may be wrong, I got B ^ 2 / 2
Methods: let P (m, n)
m^2+n^2=OP^2=c^2
m^2/a^2+n^2/b^2=1
The result is: | n | = B ^ 2 / C
So area: 1 / 2 * c * | n | = B ^ 2 / 2
M is the point on the ellipse x ^ 2 / 9 + y ^ 2 / 4 = 1, F1 and F2 are the two focuses of the ellipse, I is the heart of △ mf1if2, extend Mi to intersect F1F2 in N, then | mi |: | in | =?
Mi: in = MF1: F1C = MF2: f2n (angular bisector theorem)
The two comparisons on the right come out with the sum ratio theorem
It is known that M is a point on the ellipse x2a2 + y2b2 = 1 (a ＞ B ＞ 0), and the two focal points are F1 and F2. Point P is the inner part of △ mf1f2, connecting MP and extending the intersection F1F2 to N, then the value of | MP | PN | is ()
A. aa2−b2B. ba2−b2C. a2−b2bD. a2−b2a
As shown in the figure, connect Pf1 and PF2. In △ mf1p, f1p is the angular bisector of mf1n. According to the property theorem of angular bisector in triatriatriangles, according to the property theorem of triangular interior angular bisector, according to the property theorem of angular bisector in a triangle, MP according to the equal ratio theorem, MP, PN, MF
RELATED INFORMATIONS
- 1. Given that M is the point on the ellipse x ^ 2 / 5 + y ^ 2 / 4 = 1, F1 and F2 are the two focal points of the ellipse. If the angle f1mf2 = 30 °, try to find the area of triangle mf1f2
- 2. P is any point on the hyperbola X / 16-y / 9 = 1 which is different from the vertex. F1F2 is the two focuses of the hyperbola. The trajectory equation of the center of gravity of △ pf1f2 is obtained
- 3. Given that the ellipse x2a2 + Y29 = 1 (a > 0) and hyperbola x24 − Y23 = 1 have the same focus, then the value of a is () A. 2B. 10C. 4D. 10
- 4. Given that P is any point of hyperbola x ^ 2 / 2-y ^ 2 = 1, find the minimum distance between point a (m, 0) (M > 0) and point P?
- 5. If the left and right focus of the ellipse X & # 178 / 4 + Y & # 178 / 3 = 1 is F1F2 and P (x, y) is on the ellipse, then the value range of vector Pf1 * vector PF2?
- 6. If P is a point on the ellipse, the vector Pf1 × vector PF2 =? Needs a general conclusion, and F1F2 is the focus
- 7. When the angle f1pf2 is the largest, the tangent of the angle pf1f2 is 2, Find the size of eccentricity
- 8. How to find the shortest distance between focus and ellipse? How to judge which point on the ellipse has the shortest distance to the focus? How to find the shortest distance from the point to the focus?
- 9. Why is the shortest distance from the focus of the ellipse to the end of the minor axis?
- 10. How to prove that the sum of distances between any point and two focal points of an elliptic equation is 2a by using the distance formula between two points? The elliptic equation is (x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1) No soy sauce!
- 11. Given that point a (- 2,0) B (0,2), C is any point on the circle x ^ 2 + y ^ 2 + 2x = 0, then the maximum area of triangle ABC is?
- 12. Find the maximum and minimum values of the function f (x, y) = x ^ y (4-x-y) in the closed region D bounded by the straight line x + y = 6, y = 0, x = 0
- 13. Let X and y satisfy the constraint conditions {- x + Y-2 ≤ 0, x + y-4 ≤ 0, x-2y + 2 ≤ 0} if the sum of the maximum and minimum of the objective function z = ax + y (a > 0) is 5 / 2, then the value of real number a is
- 14. When x and y are the values, the square of x plus the square of Y minus 4x plus 6y plus 18 has the minimum value, and this minimum value can be obtained
- 15. Given that the circle x + y + x-6y + M = 0 and the line x + 2y-3 = 0 intersect at P and Q, whether there is a real number m, such that PQ is the diameter
- 16. The ellipse is x ^ 2 / 25 + y ^ 2 / 9 = 1, point a is (4,0) and B is (3,1). Find a point P on the ellipse to minimize | Pb | + 5 / 4 | PA |
- 17. Let (x, y) be the point of ellipse x ^ 2 / 16 + y ^ 2 / 9 = 1, then what is the maximum value of 3x-4y ___________ thank you
- 18. Given two points a (- 2,0), B (0,2), point P is any point on the ellipse x ^ 2 / 16 y ^ 2 / 9 = 1, then the maximum distance from point P to line ab
- 19. Find the maximum length of the chord AP of a point a (1,0) on the ellipse x ^ 2 + 4Y ^ 2 = 4 Sorry, it's (0, 1) wrong. Sorry
- 20. Given the nonnegative real number x, YZ satisfies X-1 / 2 = 2-y / 3 = Z-3 / 4, w = 3x + 4Y + 5Z. Find the maximum and minimum value of wde