It is known that the left and right focal points of the hyperbola x ^ 2 / 9-y ^ 2 / 16 = 1 are F1 and F2 respectively. If there is a point P on the hyperbola, then | Pf1 | times | PF2 | = 32 Try to find the area of triangle f1pf2

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• 1. If the distance from point P to focus F1 on hyperbola x236 − Y2100 = 1 is equal to 7, then the distance from point P to another focus F2 is 7______ ．
• 2. If F1 and F2 are the two focal points of hyperbola x ^ 2 / 9-y ^ 2 / 16 = 1, if the distance between a point m on the hyperbola and one of its focal points is equal to 16, find the distance between the other focal point
• 3. Let F1 and F2 be the two focuses of hyperbola x2a2 − y2b2 = 1 (a > 0, b > 0). If F1, F2 and P (0, 2b) are the three vertices of an equilateral triangle, then the eccentricity of hyperbola is______ ．
• 4. It is known that the focus of the hyperbola X & # 178 / / A & # 178; - Y & # 178 / / B & # 178; = 1 is F1 and F2, And the point P on the hyperbola satisfies that Pf1 is perpendicular to PF2, Pf1 = 3, PF2 = 4?
• 5. The two focuses of hyperbola x squared / 9 - y squared / 16 = 1 are f1.f2, Point P is on hyperbola. If Pf1 is perpendicular to PF2, what is the distance from point P to X axis The answer in the book is 16 / 3
• 6. Let F 1 and F 2 be the two focuses of the hyperbola x ^ 2 / 4-y ^ 2 = 1, and point p be on the hyperbola If ∠ f1pf2 = 120 °, calculate the area of triangle f1pf2 Find the area of | Pf1 | PF2 | Find the minimum value of | Pf1 | PF2 |. It's wrong.
• 7. Let F1 and F2 be the left and right focus of hyperbola (x ^ 2) - (y ^ 2 / 9) = 1 respectively Let F1 and F2 be the left and right focus of hyperbola (x ^ 2) - (y ^ 2 / 9) = 1 respectively. If P is on hyperbola and Pf1 vector * PF2 vector = 0, then | Pf1 vector + PF2 vector | =? The answer is 2 root 10. But I can't work it out
• 8. It is known that the points F1 and F2 are the left and right focal points of the hyperbola x square, a square, y square and b square = 1 respectively. The line passing through F2 and perpendicular to the X axis and If the hyperbola intersects at two points AB, if Abf1 is an acute triangle, then the value range of eccentricity of the triangle yes
• 9. As shown in the figure, it is known that F1 and F2 are the two focal points of the hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 (a > 0, b > 0). Through F2, make a straight line perpendicular to the X axis, and the hyperbola intersects at point P, with the angle pf1f2 = 30 ° to solve the asymptote equation of the hyperbola
• 10. It is known that the points F1 and F2 are the left and right focus of hyperbola (x ^ 2) / (a ^ 2) - (y ^ 2) / (2) = 1 (a > 0), respectively. Through F2, the direction of the focus perpendicular to the X axis is made, and the intersection hyperbola is% 1 If △ f1ab is an equilateral triangle, the asymptote equation of the hyperbola is obtained
• 11. Given that F1 and F2 are the left and right focus of hyperbola C: x2-y2 = 1, point P is on C, and angle f1pf2 = 60 degrees, then the value of | Pf1 | multiplied by | PF2 | is How is it wrong to use the area bridge: 1 / 2 | Pf1 | multiply | PF2 | sin60 = b-cot60 / 2, which is different from the answer
• 12. It is known that F1 and F2 are the left and right focal points of hyperbola C: x2-y2 = 1, and point P is on C, ∠ f1pf2 = 60 °, then | Pf1 | · | PF2 | = () A. 2B. 4C. 6D. 8
• 13. There is a point P on the hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1, F1F2 is the left and right focus of the hyperbola, the angle f1pf2 = 90 ° and the three sides of the triangle f1pf2 The eccentricity of hyperbola can be determined by the arithmetic sequence
• 14. Let F1F2 be the focus of the hyperbola X / 4 minus y, p be on the hyperbola, and
• 15. It is known that F1F2 is the two focal points of the hyperbola x2 / 4-y2 = 1, and the point P is on the hyperbola and satisfies the angle f1pf2 = 90 ° to find the s triangle f1pf2
• 16. F1F2 is the left and right focus of the hyperbola, P is a point on the hyperbola, angle f1pf2 = 60 degrees, triangle pf1f2 = 12 √ 3, and eccentricity is 2
• 17. It is known that the two focal points of hyperbola x ^ 2 / 9-y ^ 2 / 16 = 1 are F1 and F2 respectively, the point P is on the hyperbola, and | Pf1 | x | PF2 | = 32, so the size of angle f1pf2 is calculated
• 18. It is known that the sum of the distances between the moving point P and the two focuses F1 and F2 of hyperbola 2x ^ 2-2y ^ 2 = 1 is 4 (1) The equation of trajectory C of moving point P is obtained; (2) If M is the moving point on the curve C, take M as the center and MF2 as the radius to make the circle M. if there are two intersections between the circle m and the Y axis, calculate the value range of abscissa of the point M
• 19. It is known that the left and right focus of hyperbola x ^ 2-2y ^ 2 = 2 are F1 and F2 respectively, and the moving point P satisfies the condition | Pf1 | + | PF2 | = 4 Let the locus e of the L intersection of the moving straight line passing through F2 and not perpendicular to the coordinate axis be at two points a and B. ask if there is a point D on the line of2, so that the parallelogram with DA and DB as the adjacent sides is a diamond? Make a judgment and prove it
• 20. 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/