The chord passing through the focus of the parabola and perpendicular to the axis of symmetry is called the path of the parabola. Find the equation of the parabola whose vertex is at the origin and the path length is 8 Because the topic didn't give the focus position, it was discussed in four situations . How do we get 2p = 8?

The chord passing through the focus of the parabola and perpendicular to the axis of symmetry is called the path of the parabola. Find the equation of the parabola whose vertex is at the origin and the path length is 8 Because the topic didn't give the focus position, it was discussed in four situations . How do we get 2p = 8?

Definition of parabola

In an ellipse, if the circle with the focus F1 and F2 as the two ends of the diameter just passes through the two vertices of the minor axis, the eccentricity e of the ellipse is equal to______ ．

Let the equation of the ellipse be x2a2 + y2b2 = 1 (a ＞ B ＞ 0), and the focus is F1 (- C, 0), F2 (C, 0), where C = A2 − B2. ∵ the circle with diameter F1F2 just passes through the two vertices of the minor axis, and the distance from the endpoint of the minor axis to the origin is equal to half of the focal length, that is, B = C, A2 − C2 = C, and a = 2C is simplified, so the eccentricity of the ellipse e = CA = 22