The two focuses of hyperbola x2a2 − y2b2 = 1 (a > 0, b > 0) are F1 and F2. If P is the upper point and | Pf1 | = 2 | PF2 |, the value range of hyperbolic eccentricity is () A. （1，3）B. （1，3]C. （3，+∞）D. [3，+∞]

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• 1. If | PF2 | ^ 2 / | Pf1 | = 8a, what is the range of eccentricity
• 2. 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
• 3. 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
• 4. 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
• 5. 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 |
• 6. (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)
• 7. 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
• 8. 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______ ．
• 9. 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
• 10. 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
• 11. Hyperbola: two focuses of x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (a > 0, b > 0) are F1, F2, P are a point on the hyperbola, and Pf1 = 3PF2, then the value range of eccentricity
• 12. Given that the left and right focus of hyperbola are F1 and F2 respectively, P is a point on hyperbola, and Pf1 ⊥ PF2, pf1pf2 = 4AB, then the eccentricity of hyperbola is ■
• 13. The left and right focus of the hyperbola x ^ 2 △ a ^ 2-y ^ 2 △ B ^ 2 = 1 is F1 and F2. The point P is on the hyperbola, and Pf1 = 4 is known. The maximum value of the eccentricity of the hyperbola is obtained The options are a.4 / 3 B.3 / 2 C.5 / 3 D.2
• 14. It is known that the two focuses of the hyperbola are F1, F2, one of the imaginary axes, the endpoint B, and the angle f1bf2 = 2 π / 3, so the eccentricity of the hyperbola can be obtained
• 15. If there are three different points on the line L, so that the equation x ^ 2 vector OA + X vector ob + vector BC = vector 0 has a solution, (o is not on L), find the real number solution set x^2*OA+x*OB+BC=0 BC=-(x^2*OA+x*OB) BC=OC-OB OC-OB=-(x^2*OA+x*OB) OC= - x^2*OA - x*OB + OB Because three points are collinear - x^2 - x* +1=1 - x^2 - x*=0 x(x+1)=0 X = 0 or 1 Because when x = 0, the three points coincide, which is not in line with the meaning of the topic So x = - 1 Why? OC= - x^2*OA - x*OB + OB Because three points are collinear So - x ^ 2 - x * + 1 = 1
• 16. Given that the line y = x + 1 and parabola y2 = ax intersect at two points a and B, if OA vector multiplies ob vector = A2-1, find the value of real number a
• 17. Given that the left and right focal points of hyperbola x ^ 2 / 9-y ^ 2 / 16 = 1 are F1 and F2 respectively, P is a point on the right branch of hyperbola, and | PF2 | = | F1F2 |, then the area of triangle pf1f2 is: (as long as the answer is good)
• 18. The equation of known curve is x ^ 2 / 16-y ^ 2 / 8 = 1, point P is on hyperbola, and the distance to one of focus F1 is 10, point P is on hyperbola And the distance to one of the focal points F1 is 10, and point n is the midpoint of Pf1. Find the size of / on / (o is the origin coordinate)
• 19. It is known that P is a point on the hyperbola X / 16-y / 9 = 1 with F1 and F2 as the focus, and the trajectory equation of the center of gravity g of △ f1f2p is obtained RT
• 20. It is known that F1 and F2 are the two focuses of the hyperbola x ^ 2 / 16 - y ^ 2 / 9 = 1, and P is a point on the hyperbola, It is known that F1 and F2 are two focal points of hyperbola x ^ 2 / 16 - y ^ 2 / 9 = 1, P is a point on hyperbola, and Pf1 ⊥ PF2. Find the area of △ pf1f2