过椭圆x^2/4 +y^2=1的右焦点,且斜率k=-1的直线l,交椭圆于A,B两点,求|AB|的值
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![过椭圆x^2/4 +y^2=1的右焦点,且斜率k=-1的直线l,交椭圆于A,B两点,求|AB|的值](/uploads/image/z/5925995-35-5.jpg?t=%E8%BF%87%E6%A4%AD%E5%9C%86x%5E2%2F4+%2By%5E2%3D1%E7%9A%84%E5%8F%B3%E7%84%A6%E7%82%B9%2C%E4%B8%94%E6%96%9C%E7%8E%87k%3D-1%E7%9A%84%E7%9B%B4%E7%BA%BFl%2C%E4%BA%A4%E6%A4%AD%E5%9C%86%E4%BA%8EA%2CB%E4%B8%A4%E7%82%B9%2C%E6%B1%82%7CAB%7C%E7%9A%84%E5%80%BC)
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过椭圆x^2/4 +y^2=1的右焦点,且斜率k=-1的直线l,交椭圆于A,B两点,求|AB|的值
过椭圆x^2/4 +y^2=1的右焦点,且斜率k=-1的直线l,交椭圆于A,B两点,求|AB|的值
过椭圆x^2/4 +y^2=1的右焦点,且斜率k=-1的直线l,交椭圆于A,B两点,求|AB|的值
x^2/4 +y^2=1
a=2,b=1,c=√3
右焦点F(√3,0)
k=-1
L:y=-(x-√3)=-x+√3,x=√3-y
x^2/4 +y^2=1
x^2+4y^2=4
(√3-y)^2+4y^2=4
7y^2-2√3y-1=0
xA+xB=2√3/7,xA*xB=-1/7
(yA-yB)^2=(xA-xB)^2=(xA+xB)^2-4xA*xB=(2√3/7)^2+4/7=40/49
AB^2=2(xA-xB)^2=2*40/49
|AB|=4√5/7