Know m from the meaning of the question? 1, ∴m=2, and the analytical formula of ∴ parabola is y=? X2x, ∫ point B(2, n) is on a parabola.
y=？ On x2x where ∴n=4, the coordinate of point ∴B is (2,4).
(2)? Let the analytical formula of straight line OB be y=k 1x, and the analytical formula of straight line OB is as follows.
Y=2x, and point ∵A is the intersection of parabola and X axis, so the value of point A can be obtained.
The coordinate is (10,0). If the coordinate of point P is (a,0), the coordinate of point E is
(a, 2a), according to the meaning of the question, make an isosceles right triangle PCD, as shown in figure 1. Cociu
The coordinates of point C are (3a, 2a). From point C on the parabola, we can get
2a=(3a)2？ Is that 3a? A2a=0, and a 1=? 22/9，a2=0
(give up), ∴OP=? 22/9。
(2) Make an isosceles right triangle QMN according to the meaning of the question, and let the analytical formula of straight line AB be y=k2x? B, from point A (10,0),
At point B (2,4), the analytical formula of straight line AB is y=? - 1/2? x+？ 5. When point P moves to t seconds, they are isosceles.
A right triangle has one side exactly on the same straight line, and there are the following three situations:
The first case: CD and NQ are on the same straight line. As shown in figure 2. It can be proved that △DPQ is an isosceles right triangle.
Angular. At this time, the lengths of OP, DP and AQ can be expressed as t, 4t and 2t units in turn. ∴PQ=DP=4t，
∴t？ +4t+？ 2t= 10,∴t=？ 10/7。
The second case: PC and MN are on the same straight line. As shown in figure 3. It can be proved that △PQM is an isosceles right triangle.
Angular. At this time, the lengths of OP and AQ can be expressed as t and 2t units in turn. ∴OQ= 10？ -2t, the point ∵F is at.
AB, ∴FQ=t, ∴MQ=2t, ∴ PQ = MQ = 2t, ∴t+? 2t+？ 2t= 10,∴t=2。
In the third case, when point P and point Q coincide, PD and QM are on the same straight line, as shown in Figure 4. At this point,
The length of AQ can be expressed in units of t and 2t in turn. ∴t？ +2t= 10,∴t=？ 10/3。 To sum up, it fits the meaning of the question.
The values of t are 10/7 respectively. ,2, 10/3。