Bring ABC three-point coordinates into the parabolic equation and get a parabola:
y=x^2+4x+3
2
P is a point on a parabola, so when P is (-4, m), m=3.
Q is a point on a straight line, which intersects with the X axis to get the coordinates of point Q (4,0).
PC is parallel to OQ, and PC=OQ=4. PCQO is a parallelogram.
∠OPC=∠AQC
3、
Suppose the ordinate of n is h.
Then s δ AMN = 1/2 am h.
AM=3t
h=OC-sin∠AQCXt=3-3/5t
sδamn=4.5t( 1-0.2t)=-0.9t^2+4.5t
T=2.5 is the largest area, but considering
3t = < AQ,t = < CQ。
Let t=7/3, at this time, S=5.6.
If PQ divides MN vertically, there must be QN=QM.
QN=5 tons
QM=7-3t
At this time t= 1.
The coordinate of m at this time is (0,0 0) n at this time is (0.8,2.4).
PQ crosses the midpoint of MN (0.4, 1.2).
Get the straight line k=- 1/3.
y=- 1/3(x-4)
Substitution parabola
3x 2+ 13x+5 = 0。
P (-0.4438+05538+0848 24438+06, 1)。 48638.86668666667
Or (-3.99438+0538+04092,2). 39936.88868886666