如图,已知抛物线y=x²+3x-4与x轴交于A,B两点，与y轴交于C点，直线y=2x+2与抛物线交于
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(1)二者的底相同(DE)，只需其上的高相等即可，即CP与DE平行。CP的斜率也是2，C(0, -4), CP的方程为y = 2x - 4 (点斜式)y = 2x - 4 =x²+3x-4x = -1 (另一解x = 0为点C)P(-1, -6)
(2)x²+3x-4 = 2x + 2,x²+ x - 6 = (x + 3)(x - 2) = 0D(-3, -4), E(2, 6)
DE = 5√5, CF = 2 - (-4) = 6
P(p, p²+3p-4)CFP的面积a = (1/2)*CF*|p| = 3|p|P与y = 2x + 2 (2x - y + 2 = 0)的距离h = |2p - p²-3p+4|/√[2² + (-1)²] = |p² + p - 4|/√5DEP的面积b = (1/2)*DE*h = (5/2)|p² + p - 4|a = b5|p² + p - 4| = 6|p|5p² + 5p - 20 = ±6p
其余自己做。
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