![](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>)
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
The abscissa of point P is C, because the hyperbola intersected by a straight line perpendicular to the x-axis is made through F2. Substituting it into the equation: C ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1, because: C ^ 2 = a ^ 2 + B ^ 2, we can get: (a ^ 2 + B ^ 2) / A ^ 2-y ^ 2 / b ^ 2 = 1, we can get the solution: | y | = B ^ 2 / A, so | PF2 | = B ^ 2 / A, because: | F1F2 | = 2c, and ∠ pf1f2 = 30 °, so we have
RELATED INFORMATIONS
- 1. 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
- 2. If the chord AB length of the left focus F1 passing through the hyperbola X / 16-y / 9 = 1 is 6, then the perimeter of △ abf2 (F2 is the right focus) is () A 28 B 22 C 14 D12
- 3. If the chord AB length of the left focus F1 passing through the hyperbola x216 − Y29 = 1 is 6, then the perimeter of △ abf2 (F2 is the right focus) is 6______ ．
- 4. Through hyperbola x ^ 2 / 16-y ^ 2 / 9 = 1, the chord AB length of left focus F1 is 5?
- 5. If the chord AB length of the left focus F1 passing through the hyperbola x216 − Y29 = 1 is 6, then the perimeter of △ abf2 (F2 is the right focus) is 6______ ．
- 6. If the focus coordinates of hyperbola y ^ 2 / A ^ 2-x ^ 2 / b ^ 2 = 1 are F1, F2, the length of chord AB passing through F1 is 6, the perimeter of triangle abf2 is 28, e = 5 / 4, find a If the focus coordinates of hyperbola y ^ 2 / A ^ 2-x ^ 2 / b ^ 2 = 1 are F1, F2, the length of chord AB passing through F1 is 6, the perimeter of triangle abf2 is 28, and E = 5 / 4, find the value of a and B
- 7. The left and right focus F1, F2 of hyperbola x squared △ 25 minus y squared △ 9 = 1, the length of chord AB passing through F1 is 2, find the circumference of triangle abf2
- 8. Through the left focus F1 of hyperbola x ^ 2 / 3-y ^ 2 = 1, make the chord AB with inclination angle of π / 3. Find the perimeter of triangle f2ab
- 9. There are three points a (2,1), B (6,2), C (3, - 3) in the plane rectangular coordinate system
- 10. If vector a (1,2) B (4,3) C (- 2,5), then what is the shape of triangle ABC, if it is changed to B (2,2)
- 11. 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
- 12. 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
- 13. 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.
- 14. 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
- 15. 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?
- 16. 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______ ．
- 17. 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
- 18. 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______ ．
- 19. 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
- 20. 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