As shown in the figure, in the plane rectangular coordinate system, a (- 3,0), point C is on the positive half axis of Y axis, BC ‖ X axis, and BC = 5, AB intersects Y axis at point D, OD = 32 (1) (2) the parabola passing through three points a, C and B intersects with the x-axis at point E and connects with be. If the moving point m starts from point a and moves in the positive direction of x-axis, and the moving point n starts from point E and moves at a constant speed on the straight line EB, the moving speed is one unit length per second. When the moving time t is, the △ mon is a right triangle

As shown in the figure, in the plane rectangular coordinate system, a (- 3,0), point C is on the positive half axis of Y axis, BC ‖ X axis, and BC = 5, AB intersects Y axis at point D, OD = 32 (1) (2) the parabola passing through three points a, C and B intersects with the x-axis at point E and connects with be. If the moving point m starts from point a and moves in the positive direction of x-axis, and the moving point n starts from point E and moves at a constant speed on the straight line EB, the moving speed is one unit length per second. When the moving time t is, the △ mon is a right triangle

(1) The coordinates of ∵ BC ∥ X axis, ∥ BCD ∥ AOD, ∥ cdod = bcao, ∥ CD = 53 × 32 = 52, ∥ co = 52 + 32, ∥ C point are (0, 4). (2) as shown in Fig. 1, if BF ⊥ X axis is at point F, then BF = 4, EF = 3, ∥ be = 5, OE = 8, AE = 11 from the symmetry of parabola. According to the motion direction of point n, it can be discussed in the following two cases: ① point n is on ray EB, if ≁ NMO = 90 °, as shown in Fig. 1, then cos = 4 If ∠ NOM = 90 ° as shown in Fig. 2, then points n and G coincide, ∵ cos ∠ bef = oege = FEBE, ∵ 8t = 35, t = 403, ∵ Onm = 90 ° as shown in Fig. 3, then cos ∠ NEM = cos ∠ bef, ∵ men = FEBE, ∵ t − 11T = 35, t = 552, and ∠ NOM = 90 ° and ∠ NOM = 90 ° as shown in Fig. 3 In conclusion, when t = 558, t = 403 or T = 552, △ mon is a right triangle

The straight line y = 2x + 5 intersects with the parabola y ^ 2 = - 4x at two points a and B, and O is the origin of the coordinate to find the area of the triangle OAB
I have worked out AB = root 55. How do you calculate OB and OA,

AB=√55
That is, the bottom edge is √ 55
And the height is the distance from O to 2x-y + 5 = 0
So h = | 0-0 + 5 | / √ (2 & # 178; + 1 & # 178;) = √ 5
So area = 5 √ 11 / 2