已知抛物线y=ax2+bx+c的对称轴为直线x=2,且与x轴交于A、B两点,与y轴交于点C,其中A(1,0),C(0,-3)
(1)求抛物线的解析式;(2)若点P在抛物线上运动(点P异于点A).①如图1.当△PBC面积与△ABC面积相等时.求点P的坐标;②如图2.当∠PCB=∠BCA时,求直线C...
(1)求抛物线的解析式;
(2)若点P在抛物线上运动(点P异于点A).
①如图1.当△PBC面积与△ABC面积相等时.求点P的坐标;
②如图2.当∠PCB=∠BCA时,求直线CP的解析式.
(2)若点P在抛物线上运动(点P异于点A).
①如图1.当△PBC面积与△ABC面积相等时.求点P的坐标;
②如图2.当∠PCB=∠BCA时,求直线CP的解析式. 展开
(2)若点P在抛物线上运动(点P异于点A).
①如图1.当△PBC面积与△ABC面积相等时.求点P的坐标;
②如图2.当∠PCB=∠BCA时,求直线CP的解析式.
(2)若点P在抛物线上运动(点P异于点A).
①如图1.当△PBC面积与△ABC面积相等时.求点P的坐标;
②如图2.当∠PCB=∠BCA时,求直线CP的解析式. 展开
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(1) 对称轴为直线x=2, y = a(x - 2)² + d
x = 1, y = a + d = 0
x = 0, y = 4a + d = -3
a = -1, d = 1
y = -(x - 2)² + 1 = -xy = -x² + 4x - 3 = -(x - 1)(x - 3)
A(1, 0), B(3, 0)
(2)
①△PBC面积与△ABC面积相等时, AB为共同的底,只顷凳须高相同,即P, C纵坐标相等
-x² + 4x - 3 = -3
x = 4 (舍去0)
②厅乎衡BC为角ACP的平分线
AC的解析式: x - y/3 = 1, 3x - y - 3 = 0
设CP斜率为k, 解析式y = kx - 3, kx - y - 3= 0
B与二者距离相等:
|9 - 0 - 3|/扮做√(9 + 1) = |3k - 0 - 3|/√(k² + 1)
3k² - 10k + 3 = 0
(3k - 1)(k - 3) = 0
k = 1/3 (舍去k = 3, 此时CP与AC重合)
直线CP的解析式: y = x/3 - 3
x = 1, y = a + d = 0
x = 0, y = 4a + d = -3
a = -1, d = 1
y = -(x - 2)² + 1 = -xy = -x² + 4x - 3 = -(x - 1)(x - 3)
A(1, 0), B(3, 0)
(2)
①△PBC面积与△ABC面积相等时, AB为共同的底,只顷凳须高相同,即P, C纵坐标相等
-x² + 4x - 3 = -3
x = 4 (舍去0)
②厅乎衡BC为角ACP的平分线
AC的解析式: x - y/3 = 1, 3x - y - 3 = 0
设CP斜率为k, 解析式y = kx - 3, kx - y - 3= 0
B与二者距离相等:
|9 - 0 - 3|/扮做√(9 + 1) = |3k - 0 - 3|/√(k² + 1)
3k² - 10k + 3 = 0
(3k - 1)(k - 3) = 0
k = 1/3 (舍去k = 3, 此时CP与AC重合)
直线CP的解析式: y = x/3 - 3
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