The two foci F1, F2 and P of hyperbola x2 / 4-y2 / B2 = 1 are the points on the hyperbola, Pf1, F1F2 and PF2 form an arithmetic sequence, and op = 5, then B ^ 2 =?
Let Pf1 = m, PF2 = M-4, then M + M-4 = 4C, and (2op) ^ 2 + F1F2 ^ 2 = 2 (m ^ 2 + (M-4) ^ 2)
So 100 + (m-2) ^ 2 = 2m ^ 2 + 2 (M-4) ^ 2, the solution is 3M ^ 2-12m-72 = 0, M = 2 + 2, root 7
b^2=c^2-4=(0.5m-1)^2-4=3
RELATED INFORMATIONS
- 1. The two focuses of hyperbola x ^ 2 / 4-y ^ 2 / b ^ 2 = 1 are F1 and F2, and point P is on the hyperbola, if | Pf1 | F1F2 | PF2 | is an arithmetic sequence And | 0P | = 5, then B ^ 2=
- 2. The two foci F1, F2, P of hyperbola (x ^ 2) / 4 - (y ^ 2) / (b ^ 2) = 1 (B ∈ n *) are a point on the hyperbola, / op / < 5, / Pf1 /, / F1F2 /, / PF2 / are in equal proportion sequence, and the equation of the hyperbola is obtained
- 3. It is known that P is a point on the hyperbola x ^ 2 / 4-y ^ 2 / b ^ 2, F1 and F2 are the left and right focal points, the three sides of ⊿ P F1F2 grow into an arithmetic sequence, and ∠ F1 P F2 = 120 to calculate the value of E E is the eccentricity-
- 4. The distance from one focus to two focuses on the ellipse is D1 D2, and the focal length is 2C. If D1 2C D2 is an arithmetic sequence, the eccentricity of the ellipse can be calculated
- 5. If the distance from a point m on the parabola y = 4x2 to the focus is 1, then the ordinate of point m is () A. 1716B. 1516C. 78D. 0
- 6. If the distance from a point m on the parabola y = 4x2 to the focus is 1, then the ordinate of point m is () A. 1716B. 1516C. 78D. 0
- 7. If the distance from a point m on the parabola y = 4x2 to the focus is 1, then the ordinate of point m is () A. 1716B. 1516C. 78D. 0
- 8. If the distance from a point m on the parabola y = 4x2 to the focus is 1, then the ordinate of point m is () A. 1716B. 1516C. 78D. 0
- 9. The square of parabola y = 2px (P > 0), the distance from a point m to the focus is a (a > P / 2), then what is the distance from point m to the collimator? The abscissa of point m is If the distance between a point m and the focus on the parabola y = 2px (P > 0) is a (a > P / 2), what is the distance between the point m and the collimator? What is the abscissa of the point m?
- 10. If the abscissa of a point m on the parabola y2 = 16x is 6, then the distance from m to the focus f is 0______ .
- 11. If the ratio of the distance from a vertex of hyperbola to the corresponding quasilinear to the distance from this point to another focus is λ, then the value range of λ is? No derivative algorithm
- 12. If the distance from a point P on the hyperbola x2 / 64 - Y2 / 36 = 1 to the right focus of the hyperbola is 4, then the distance from point P to the left focus of the hyperbola is? If the distance between point P and its right focus is 17, then the distance between point P and its left focus is? It needs to be explained in detail
- 13. On the hyperbola x2 / 16-y2 / 9 = 1, a point P makes it twice as far from the left focus as it is from the right focus
- 14. On hyperbola x2 − y216 = 1, the distance from a point P to one of its focal points is equal to 4, then the distance from point P to another focal point is equal to 4______ .
- 15. If the distance from a point P on the hyperbola x2 / 25-y2 / 9 = 1 to one focus is 15, then the distance from it to another focus is 15
- 16. If the distance from a point P on the hyperbola x24 − Y22 = 1 to the right focus of the hyperbola is 2, then the distance from point P to the Y axis is () A. 463B. 263C. 26D. 23
- 17. Given that there is a point P (6, m) on the hyperbola x2 / 9-y2 / 16 = 1, what is the distance from the point P to the right focus? If you can, give me a more complete process
- 18. In the plane rectangular coordinate system xoy, it is known that the abscissa of a point m on the hyperbola x2 / 4-y2 / 12 = 1 is 3, then the distance from m to the right focus of the hyperbola is? If the abscissa of a point m on the hyperbola x2 / 4-y2 / 12 = 1 in the plane rectangular coordinate system xoy is 3, then the distance from m to the right focus of the hyperbola is? Through point a (60), make straight line L and hyperbola x2 / 16-y2 / 4 = 1 intersect at B C. two points a are the midpoint of line BC, then the equation of straight line L is? Through point a (6,1), make straight line L and hyperbola x2 / 16-y2 / 4 = 1 intersect at B C. two points a are the midpoint of line BC, then the equation of straight line L is?
- 19. Given that the ratio of the distance between the left and right focal points of point m and hyperbola x216 − Y29 = 1 is 2:3, the trajectory equation of point m is______ .
- 20. Let {an} be an equal ratio sequence with the first term of 1 and the common ratio of - 2, then a1 + | A2 | + a3 + | A4|