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It is known that the right focus of hyperbola x2a2 − y2b2 = 1 (a > 0, b > 0) is F. if there is only one intersection point between the straight line passing through point F and the right branch of hyperbola with an inclination angle of 60 ° and the right branch of hyperbola, then the value range of eccentricity of hyperbola is () A. （1，2]B. （1，2）C. [2，+∞）D. （2，+∞）
It is known that the right focus of hyperbola x2a2 − y2b2 = 1 (a ＞ 0, B ＞ 0) is F. if there is only one intersection point between the straight line passing through point F and the right branch of hyperbola, the absolute value of the slope of the straight line is less than or equal to the slope of asymptote Ba, BA ≥ 3, eccentricity E2 = c2a2 = A2 + b2a2 ≥ 4, and E ≥ 2
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- 1. It is known that the right focus of hyperbola x2a2 − y2b2 = 1 (a > 0, b > 0) is F. if there is only one intersection point between the straight line passing through point F and the right branch of hyperbola with an inclination angle of 60 ° and the right branch of hyperbola, then the value range of eccentricity of hyperbola is () A. （1，2]B. （1，2）C. [2，+∞）D. （2，+∞）
- 2. Known hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0b)
- 3. It is known that F 1 and F 2 are two fixed points, P is the intersection of ellipse and hyperbola with F 1 and F 2 as the common focus, and Pf1 ⊥ PF2, E 1 and E 2 are the eccentricities of the above ellipse and hyperbola respectively, then () A. e12+e22=2B. e12+e22=4C. 1e21+1e22＝2D. 1e21+1e22＝4
- 4. Let E1 and E2 be the eccentricities of ellipses and hyperbolas with common intersections F1 and F2 respectively, p be a common point, and the segments Pf1 and PF2 are vertical Find the value of (E1 ^ 2 + E2 ^ 2) / (E1E2) ^ 2. (^ 2 is the square)
- 5. If the ellipse with eccentricity E1 and the hyperbola with eccentricity E2 have the same focus, and the end points of the major axis, the end points of the minor axis and the distance from the focus to an asymptote of the hyperbola form an equal ratio sequence, then (E1 ^ 2-1) / (E2 ^ 2-1)=
- 6. It is known that the ellipse and hyperbola have the same focus, and the two curves intersect at P, Pf1 and are perpendicular to PF2. Ask the relationship between the two eccentricities (expressed by E1 and E2 respectively) It is known that the ellipse and hyperbola have the same focus F1 and F2, and the two curves intersect at P, Pf1 is perpendicular to PF2. Ask the relationship between the eccentricity of the two curves (expressed by E1 and E2 respectively)
- 7. A point P on the hyperbola X & # 178; - Y & # 178 / 9 = 1 with F2 as the left and right focus satisfies the vector Pf1 * vector PF2 = 0 |Vector Pf1 | + | vector PF2 | =? Seek the concrete process
- 8. Let F 1 and F 2 be the left and right focal points of the hyperbola x 2-y 2 / 9 = 1 respectively. If P is on the hyperbola and pf1pf 2 = 0, then | Pf1 + PF2 | =?
- 9. It is known that P is a point on the right branch of hyperbola x2 / 16-y2 / 9 = 1, and F1 and F2 are the left and right focal points respectively. If | Pf1 |: | PF2 | = 3:2, calculate the coordinates of point P!
- 10. It is known that the two focal points of hyperbola x ^ 2 / A ^ 2-y ^ 2 = 1 (a > 0) are F1 and F2. P respectively, which are the points on the hyperbola, and ∠ f1pf2 = 90 °, find / Pf1 / * / PF2/
- 11. The right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 is F. if there is only one straight line passing through point F and inclination angle 30 and hyperbola The right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 is F. if there is only one intersection point between the straight line passing through point F and hyperbola with inclination angle of 30, the range of eccentricity of hyperbola is smaller
- 12. If the line L passes through the left focus F of hyperbola (x ^ 2) / 3-y ^ 2 = 1 (1) If there is a common point between the line L and the right branch of the hyperbola, point out the range of the inclination angle a of the line L (2) If the line L and hyperbola intersect at two points a and B, P is the midpoint of AB, O is the origin of coordinates, when the slope of OP is equal to 1 / 4, the equation of line L is obtained
- 13. Given that f is the right focus of hyperbola x216 − Y29 = 1, M is a moving point on the right branch of hyperbola, and a (5,4), the maximum value of 4mf-5ma is______ ．
- 14. It is known that F1F2 is the left and right focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0), If the triangle abf2 is an acute triangle, then the value range of eccentricity of the hyperbola
- 15. (2014 Jilin simulation) given that the right focus F of hyperbola x2a2 − y2b2 = 1 (a > 0, b > 0), the line x = A2C and its asymptote intersect at two points a and B, and △ ABF is an obtuse triangle, then the value range of hyperbolic eccentricity is () A. (3，+∞)B. (1，3)C. (2，+∞)D. (1，2)
- 16. It is known that the hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1, (a > 0, b > 0) f1.f2 is the two focal points of the hyperbola, and the point P is on the hyperbola. Find the minimum value of | Pf1 | * | PF2 |
- 17. The two focuses of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 are F1 and F2. If P is the upper point and lpf1l = 2lpf2l, the value range of hyperbolic eccentricity is
- 18. It is known that F 1 and F 2 are the focus of hyperbola x ^ / A ^ - y ^ / b ^ = 1 (a > 0, b > 0), P is on the right branch, and Pf1 = 4pf 2. The range of eccentricity of hyperbola is obtained
- 19. P is the point on the hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0), F1 and F2 are its focus, the eccentricity of the hyperbola is 5 / 4, and the vector pf * vector PF2 = 0, If the area of triangle f1pf2 is 9, find the value of a + B
- 20. If | PF2 | ^ 2 / | Pf1 | = 8a, what is the range of eccentricity