It is known that the center of the ellipse is at the origin and the focus is on the x-axis. The area of the quadrilateral obtained by connecting its four vertices is 42. Connect a point on the ellipse (except the vertex) and the four vertices of the ellipse respectively. The product of the slopes of the four straight lines where the line segment is located is 14. The standard equation of the ellipse is obtained

It is known that the center of the ellipse is at the origin and the focus is on the x-axis. The area of the quadrilateral obtained by connecting its four vertices is 42. Connect a point on the ellipse (except the vertex) and the four vertices of the ellipse respectively. The product of the slopes of the four straight lines where the line segment is located is 14. The standard equation of the ellipse is obtained

Let the obtained equation be x2a2 + y2b2 = 1 (a > b > 0), and a point on the ellipse be p (x0, Y0), then the four vertices of the ellipse are (a, 0), (- A, 0), (0, b), (0, - B), respectively. From the known slope product of four straight lines as 14, we can get y02x02-a2 · y02-b2x02 = 14, ∵ b2x02 + a2y02 = a2b2, ∩ Y02 = B2 (a2-x02) A2, X02 = A2 (b2-y02) B2, and substitute b4a4 = 14, and from the known 2Ab = 42 The elliptic equation is x24 + Y22 = 1