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
Let F 1 coordinate be (- C, 0), F 2 (C, 0)
Then the equation of parabola C is y ^ 2 = 4C (x + C), C > 0,
The Quasilinear equation of parabola C is x = - 3C,
PF1=2c,
PF2=4c,
PF1:PF2=e=2c/4c=1/2.
e=1/2.
RELATED INFORMATIONS
- 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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
- 6. 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
- 7. Elliptic equation x ^ 2 / 4 + y ^ 2 / 3 = 1, try to determine the value range of T, so that there are two different points on the ellipse symmetrical about the straight line y = 4x + t
- 8. Given the elliptic equation x ^ 2 / 2 + y ^ 2 / 3 = 1, try to determine the value range of B, so that there are two different points on the ellipse, a and B are symmetric about the straight line y = 4x + B
- 9. Analytic geometry elliptic problem: elliptic equation x ^ 2 + 1 / 2Y ^ 2 = 1, straight line y = x + B, there are two points on the ellipse symmetrical about the straight line, find the value range of B So x1-y1 + B = x2-y2 + B or x1-y1 + B = - (x2-y2 + b) That is, x1-x2 = y1-y2 or X1 + x2 = Y1 + Y2 How to x1-y1 + B = - (x2-y2 + b) to X1 + x2 = Y1 + Y2 2b is gone?
- 10. Given a point P (x, y) on the ellipse x * 2 / A * 2 + y * 2 / b * 2 = 1 (a > b > 0), find the value range of 3x + 4Y X * 2 is the square of X /Denotes divided by
- 11. 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
- 12. 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
- 13. 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
- 14. 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=
- 15. 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
- 16. 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______ .
- 17. 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
- 18. 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?
- 19. 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?
- 20. What is the midpoint coordinate of the chord cut by the ellipse x ^ 2 + 2Y ^ 2 = 4?