Given that the vertex is at the origin and the focus is on the Y-axis of the parabola C section line y = 2x-1, the chord length is 2 root sign 10, and the equation of parabola C is obtained

Let the parabolic equation and the linear equation y = 2x-1 be simultaneous
Let ax & # 178; = 2x-1, ax & # 178; - 2x-1 = 0, let the two roots of the equation be x1, X2, then
2√10＝√﹛﹙x1－x2﹚²＋﹙y1－y2﹚²﹜,
40＝﹙x1－x2﹚²＋﹙y1－y2﹚²＝﹙x1－x2﹚²＋2²·(x1－x2)²＝5﹙x1－x2﹚²,
﹙x1－x2﹚²＝8,∴﹙x1＋x2﹚²－4x1x2＝8,①
∵x1＋x2＝2/a,∵x1x2＝(-1)/a,
The parabolic equation can be obtained by substituting the two equations into (1)

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