平面直角坐标系中,以P(2r,0)为圆心,r为半径做圆P交X轴于A,B两点,过Q点作垂直于X轴的直线:(X=5/2)(1)过原点向圆P做切线,分别求两条切线的表达式(2)圆P与直线X=5/2不相交,二次函数y=ax^2+bx+c
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![平面直角坐标系中,以P(2r,0)为圆心,r为半径做圆P交X轴于A,B两点,过Q点作垂直于X轴的直线:(X=5/2)(1)过原点向圆P做切线,分别求两条切线的表达式(2)圆P与直线X=5/2不相交,二次函数y=ax^2+bx+c](/uploads/image/z/4062990-30-0.jpg?t=%E5%B9%B3%E9%9D%A2%E7%9B%B4%E8%A7%92%E5%9D%90%E6%A0%87%E7%B3%BB%E4%B8%AD%2C%E4%BB%A5P%282r%2C0%29%E4%B8%BA%E5%9C%86%E5%BF%83%2Cr%E4%B8%BA%E5%8D%8A%E5%BE%84%E5%81%9A%E5%9C%86P%E4%BA%A4X%E8%BD%B4%E4%BA%8EA%2CB%E4%B8%A4%E7%82%B9%2C%E8%BF%87Q%E7%82%B9%E4%BD%9C%E5%9E%82%E7%9B%B4%E4%BA%8EX%E8%BD%B4%E7%9A%84%E7%9B%B4%E7%BA%BF%EF%BC%9A%EF%BC%88X%3D5%2F2%EF%BC%89%281%29%E8%BF%87%E5%8E%9F%E7%82%B9%E5%90%91%E5%9C%86P%E5%81%9A%E5%88%87%E7%BA%BF%2C%E5%88%86%E5%88%AB%E6%B1%82%E4%B8%A4%E6%9D%A1%E5%88%87%E7%BA%BF%E7%9A%84%E8%A1%A8%E8%BE%BE%E5%BC%8F%EF%BC%882%EF%BC%89%E5%9C%86P%E4%B8%8E%E7%9B%B4%E7%BA%BFX%3D5%2F2%E4%B8%8D%E7%9B%B8%E4%BA%A4%2C%E4%BA%8C%E6%AC%A1%E5%87%BD%E6%95%B0y%3Dax%5E2%2Bbx%2Bc)
平面直角坐标系中,以P(2r,0)为圆心,r为半径做圆P交X轴于A,B两点,过Q点作垂直于X轴的直线:(X=5/2)(1)过原点向圆P做切线,分别求两条切线的表达式(2)圆P与直线X=5/2不相交,二次函数y=ax^2+bx+c
平面直角坐标系中,以P(2r,0)为圆心,r为半径做圆P
交X轴于A,B两点,过Q点作垂直于X轴的直线:(X=5/2)
(1)过原点向圆P做切线,分别求两条切线的表达式
(2)圆P与直线X=5/2不相交,二次函数y=ax^2+bx+c过A,B两点,顶点在圆P上,直线Y=-ax+c与X轴交与M,当M在线段PB上运动时,求a的取值范围
图
P在X轴上,画掉了
平面直角坐标系中,以P(2r,0)为圆心,r为半径做圆P交X轴于A,B两点,过Q点作垂直于X轴的直线:(X=5/2)(1)过原点向圆P做切线,分别求两条切线的表达式(2)圆P与直线X=5/2不相交,二次函数y=ax^2+bx+c
(1) 设切线斜率为k,方程为y = kx,kx - y = 0
圆P的圆心P为(2r,0),P与 kx - y = 0的距离为圆半径r:
r = |2rk -0|/√(k² + 1)
r²(k²+1) = 4r²k²
3k² = 1
k = ±√3/3
切线方程为y = ±(√3/3)x
(2) 圆方程为(x-2r)² + y² = r²,A(r,0),B(3r,0)
圆P与直线X=5/2不相交,r > 5/2或 3r < 5/2 (r < 5/6)
y=ax^2+bx+c过A,B两点:
ar² + br + c = 0 (1)
9ar² + 3br + c = 0 (2)
(2)-(1):b = -4ar (3)
c = -ar² - br = -ar² + 4ar² = 3ar² (4)
y=ax^2+bx+c的顶点在圆P上,显然顶点为圆上纵坐标最大C(2r,r)或最小处D(2r,-r).
(a) y=ax^2+bx+c过C(2r,r)
r = 4ar² + 2br + c = 4ar² -2r*4ar + 3ar² = - ar²
a = -1/r
(b) y=ax^2+bx+c过C(2r,r)
-r = 4ar² + 2br + c = 4ar² -2r*4ar + 3ar² = - ar²
a = 1/r
直线Y= -ax+c = -ax + 3ar² = 0,x = 3r²,M(3r²,0);
当M在线段PB上运动时2r ≤ 3r² ≤ 3r,2/3 ≤ r ≤ 1
a = -1/r时, -3/2≤ a ≤ -1
a = 1/r 时,1 ≤ a ≤ 3/2