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If the half focal length of the ellipse x ^ 2 / A ^ 2 + y ^ / b ^ 3 = 1, (a > b > 0) is C, and the abscissa of the straight line y = 2x and a focus of the ellipse is exactly C, then the eccentricity of the ellipse
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- 1. How to determine the focus of the ellipse Some answer questions, Taking the long and short axis of the ellipse as the center and the short axis as the diameter, draw a circle, and the intersection of the long axis of symmetry is the focus of the ellipse.
- 2. P is the point F1 on the x-axis ellipse x2a2 + y2b2 = 1, F2 is the two focal points of the ellipse, and the half focal length of the ellipse is C, then the difference between the maximum and minimum value of | Pf1 | · | PF2 | must be () A. 1B. a2C. b2D. c2
- 3. If P is a point on a fixed ellipse (the length of major axis, the length of minor axis and the length of focal length are 2a, 2b and 2C respectively, and the focus is F1 and F2), If the maximum value of | Pf1 | PF2 | is 16 and the minimum value is 7, then what are a and B equal to? Why?
- 4. A focal point is f (2 radical 3,0), a = 2c, find the analytic expression of ellipse
- 5. It is known that the left and right focal points of ellipse C: x2a2 + y2b2 = 1 (A & gt; B & gt; 0) are F1 and F2 respectively, the eccentricity e = 12, and the line y = x + 2 passes through the left focal point F1. (1) find the equation of ellipse C; (2) if P is a point on ellipse C, find the range of ∠ f1pf2
- 6. It is known that the eccentricity of ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) e = √ 2 / 2, the left and right focal points are F1, F2 and P (2, √ 3) Let the line L: y = KX + m intersect with the ellipse C at two points M. n. the inclination angles of the lines F2m and f2n are α, β, and α + β = π (PIE). Let's ask whether the line L passes the fixed point? If so, find the coordinates of the point
- 7. It is known that the left and right focal points of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 are F1 and F2 half focal length is c. the chord f1m of the ellipse is made through F1 and extended to N, so that Mn = MF2. It is proved that the trajectory of n is a circle and its equation is solved
- 8. The two focal points of the ellipse y2a2 + x2b2 = 1 (a > b > 0) are F1 (0, - C), F2 (0, c) (c > 0), the eccentricity e = 32, and the shortest distance from the focal point to the point on the ellipse is 2-3
- 9. If the focal length, minor axis length and major axis length of an ellipse form an arithmetic sequence, then the eccentricity is______ ．
- 10. If the length of the major axis, the length of the minor axis and the focal distance of an ellipse form an arithmetic sequence, then the eccentricity of the ellipse is zero______ ．
- 11. If the projection of the two intersection points of the straight line y = 22x and the ellipse x2a2 + y2b2 = 1, a > b > 0 on the X axis is exactly the two focal points of the ellipse, then the eccentricity e of the ellipse is equal to () A. 32B. 22C. 33D. 12
- 12. If the point P (C, 2C) is in the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0), then the eccentricity of the ellipse E= Such as the title
- 13. The focal length of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 is 2C. If the three numbers a, B and C form an equal ratio sequence in turn, calculate the eccentricity E
- 14. It is known that the eccentricity of ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a is greater than B is greater than 0) is root sign 2 / 2, and its left and right focuses are F1F2 respectively. P is a point on the ellipse. Vector Pf1 × vector PF2 = 3 / 4, absolute value of OP = root sign 7 / 2 1. Solving the equation of ellipse C 2. The moving line L passing through point s (0, - 1 / 3) intersects with ellipse C and a, B. question: is there a fixed point m on the y-axis so that a circle with diameter AB passes through point m? If there is, find out the coordinates of M. if not, explain the reason
- 15. Let AB be the chord passing through the center of the ellipse and f be a focal point of the ellipse? The ellipse is x ^ 2 + 2Y ^ 2 = 1
- 16. If the hyperbola X29 − y2 = 1 has moving points P, F1 and F2, then the trajectory equation of the center of gravity m of △ pf1f2 is______ ．
- 17. There is a moving point P on the ellipse X / 9 + y2 = 1. F1 and F2 are the two focal points of the ellipse. The trajectory equation of the center of gravity m of △ pf1f2 is obtained
- 18. It is known that F 1 and F 2 are the left and right focal points of the ellipse C: x 24 + y 23 = 1 respectively, and P is the moving point on the ellipse C, then the trajectory equation of the center of gravity g of △ pf1f 2 is () A. x236+y227＝1(y≠0)B. 4x29+y2＝1(y≠0)C. 9x24+3y2＝1(y≠0)D. x2+4y23＝1(y≠0)
- 19. If the hyperbola X29 − y2 = 1 has moving points P, F1 and F2, then the trajectory equation of the center of gravity m of △ pf1f2 is______ ．
- 20. If F1 and F2 are the focus of the ellipse x ^ 2 / 25 + y ^ 2 / 16 = 1, and P is the point on the ellipse that is not on the X axis, then the trajectory equation of the center of gravity g of △ pf1f2 is