zhaobowei
幼苗
共回答了23个问题采纳率:87% 举报
(1)
长轴在x,则长轴 = 1,短轴 = 1/2,方程:x^2 + 4y^2 = 1
长轴在y,则长轴 = 2,短轴 = 1,方程:4x^2 + y^2 = 4
(2)
按题意,此时方程为:4x^2 + y^2 = 4
L斜率存在时,设为k,则L:y = kx + 1
设A(x1,y1)B(x2,y2)
则4(x1)^2 + (y1)^2 = 4或4(x2)^2 + (y2)^2 = 4
两个方程相减并整理可得:
[(y1-y2)/(x1-x2)]·[(y1+y2)/(x1+x2)] = -4
其中:[(y1-y2)/(x1-x2)] = k(AB) = k(L) = k,而P(x0,y0)是AB中点∴y1+y2 = 2y0,x1+x2=2x0
∴k·(y0/x0) = -4 ,∴k = -4x0/y0 ,代入直线方程得:
(y0)^2 = -4(x0)^2 + y0
整理可得:4[(x0) - 0]^2 + [(y0) - (1/2)]^2 = 1/4 = (1/2)^2
当L斜率不存在,即⊥x轴时,求得A、B坐标(0,2)、(0,-2),P(0,0)代入上式仍成立
∴动点P的轨迹方程是以(0,1/2)为圆心,1/2为半径的圆:4x^2 + [y-(1/2)]^2 = 1/4
1年前
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