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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
If F 1 (- C, 0), F 2 (C, 0), the vertex F 1 and focus F 2 of the parabola, then the Quasilinear x = - 3C. Furthermore, Pf1: the distance from P to the left quasilinear of the ellipse = e = [Pf1]: [PF2], so the distance from P to the left quasilinear of the ellipse = PF2, that is, the left quasilinear of the ellipse is the Quasilinear of the parabola, 3C = A & sup2 / / C, thus e = √ 3 / 3
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