標題:
locus maths 3 Q
發問:
1)the equation of two circles are given by C1:x^2 +y^2 +2x -8y=0C2: 2x^2 +2y^2 -12x -8y +18=0show that two circles intersect each other.2)a circles with centre O passes through three oints A(-5,0) B(19,0)andC(12,17)a)find the equation of the circle in the general formb)hence find the coordinates of... 顯示更多 1)the equation of two circles are given by C1:x^2 +y^2 +2x -8y=0 C2: 2x^2 +2y^2 -12x -8y +18=0 show that two circles intersect each other. 2)a circles with centre O passes through three oints A(-5,0) B(19,0)andC(12,17) a)find the equation of the circle in the general form b)hence find the coordinates of O and the radius of the circles . 3) a straight line L:kx +2y -5=0 and a circle (x-2)^2+(y-6)^2=1 ,P(1,1) is a point on L if Q is moving piont on L,which is the minimum distance between Q and the circle ?
最佳解答:
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(1) Centre of C1 = (-1, 4) Centre of C2 = (6, 4) Distance between centres = √[(-1 - 6)2 + (4 - 4)2] = 7 Radius of C1 = (1/2)√[22 + (-8)2] = √17 Radius of C2 = (1/2)√[(-12)2 + (-8)2 - 4(18)] = √34 Sum of radius = √17 (√2 + 1) > 7 Difference of radius = √17 (√2 - 1)
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