It is known that the intersection point of the parabola y2 = 4x of the common focus F2 and the ellipse C is p, the point F1 is the left focus of the ellipse and | Pf1 | = 5 If the abscissa of point P is 2, then the eccentricity e of the ellipse=

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• 1. If the left and right focuses of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 are F1 and F2, and the segments F1 and F2 are divided into 5:3 segments by the focus of the parabola y2 = 2bx, then the eccentricity of the ellipse is
• 2. The major axis length of ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) is 4, F1 and F2 are its left and right focus respectively, and the focus of parabola y2 = - 4x is F1 The line L passing through the focus F1 intersects with the ellipse at p.q. the maximum area of the triangle f2pq is calculated
• 3. It is known that the eccentricity of the ellipse e is e, the two focal points are F1 and F2, the parabola C takes F1 as the vertex, F2 as the focal point, and P is a common point of the two curves. If | Pf1 | PF2 | = e, then the value of E is () A. 33B. 32C. 22D. 63
• 4. Eccentricity of ellipse e, two focus F1F2, parabola C, take F1 as vertex, F2 as focus, P as focus of two curves, if Pf1: PF2 = e, find E
• 5. It is known that F1 and F2 are the left and right focal points of the ellipse e, and the parabola C takes F1 as the vertex and F2 as the focal point. Let p be an intersection of the ellipse and the parabola, If the eccentricity of the ellipse is e, and "Pe1" = e "PF2", then what is the value of E? Its meaning is as follows: if the left and right focus of the parabola are known, and the fixed point and focus of the parabola are known, and P is an intersection of the ellipse and the parabola, and the eccentricity of the ellipse is known, and the absolute value of Pf1 is equal to the absolute value of e multiplied by PF2, then the value of E can be obtained. Thank you for giving a detailed solution
• 6. It is known that the eccentricity of the ellipse x2 / A2 + Y2 / B2 = 1 (a > b > 0) is √ 2 / 2, and the right focus is f (1,0) If a straight line with an inclination angle of 45 ° intersects the ellipse at two points a and B, calculate the value of ab
• 7. It is known that the eccentricity of ellipse C: x2 / A2 + Y2 / B2 = 1 (a > b > 0) is 2 / 3, passing through focus f (C, 0) and point B (0, 0), Urgent, final exam
• 8. Let the eccentricity of the ellipse x2 / A2 + Y2 / B2 = 1 (a > b > 0) be e = 1 / 2, the right focus f (C, 0), equation a
• 9. The vertex of the parabola is at the origin, its directrix passes through a focus F1 of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 1), and is perpendicular to the major axis of the ellipse The vertex of the parabola is at the origin, and its quasilinear passes through a focus F1 of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 1), and is perpendicular to the major axis of the ellipse. The intersection of the parabola and the ellipse is m (2 / 3, 2 radical 6 / 3). Solve the parabola and the elliptic equation
• 10. Given that the center of the ellipse t is at the origin, the focus is on the X axis, the eccentricity is √ 3 / 2, and passes through the focus F of the parabola C: X & # 178; = 4Y, the equation of the ellipse t is solved
• 11. The parabola y2 = 2px (P > 0) and the ellipse x ^ 2 / 9 + y ^ 2 / 8 = 1 have the same focus F 2, and the two curves intersect at P and Q. F 1 is another focus of the ellipse Solving: 1) parabolic equation; 2) coordinates of P and Q; 3) area of △ pf1f2
• 12. Given that a focus of hyperbola x2a2 − y2b2 = 1 coincides with the focus of parabola y2 = 4x, and the eccentricity of the hyperbola is 5, then the asymptote equation of the hyperbola is______ ．
• 13. It is known that a focus of hyperbola x2 / a2-y2 / B2 = 1 coincides with that of parabola y2 = 4x If a focal point of x2 / a2-y2 / B2 = 1 coincides with the focal point of parabolic y2 = 4x, and the distance from the focal point to the asymptote of hyperbola is √ 3, then the equation of asymptote is
• 14. If the eccentricity of hyperbola x2 / m-y2 / N = 1 is 2 and there is a focal point coincident with that of parabola y2 = 4x, then the value of Mn is?
• 15. Given that the ellipse x ^ 2 + 2Y ^ 2 = 4 intersects with the straight line L at two points a and B, and the point is the midpoint of (1,1) chord, the equation of the straight line?
• 16. What is the midpoint coordinate of the chord cut by the ellipse x ^ 2 + 2Y ^ 2 = 4?
• 17. Given the ellipse x ^ 2 + 2Y ^ 2 = 4, find the length of the chord with (1,1) as the midpoint
• 18. Given the ellipse x ^ 2 + 2Y ^ 2 = 4, what is the length of the chord with (1,1) as the midpoint?
• 19. Let the line y = x-3 and the ellipse x ^ 2 + 2Y ^ 2 = 8 intersect at two points a and B, and find the chord length | ab | and the area of triangle ABC
• 20. As shown in Figure 4, cross a focal point (- 1,0) of the ellipse x ^ 2 + 2Y ^ 2 = 2 to make a straight line intersection ellipse a, two points o of B as the origin of the coordinates. Find the maximum area of the triangle AOB