Question

如图,抛物线Y=-X+BX+C与直线Y=1/2X+2

Answer 1

C在Y轴上,C在直线上 => C(0,2)

C,D坐标带入抛物线,有

c = 2

7/2 = -9 + 3b + c

故b = 7/2,c = 2

设P坐标(xp,-xp^2 + 7/2xp + 2)

因∠pcf = 45度,直线CF斜率为tanTheta = 1/2,则直线CP的斜率为

tan(Theta - Pi/4) = (1/2 - 1)/(1 + 1/2 * 1) = - 1/3

则直线CP方程为y = -1/3x + 2

将CP方程带入抛物线方程,有

-xp^2 + 7/2xp + 2 = -1/3xp + 2

因此xp = 0(依题设舍去)或xp = 23/6

所以P(23/6,13/18)即为所求