標題:
發問:
Two circles with equations (x+1)^2 + (y+1)^2=25 and (x-11)^2 + (y-8)^2 =100 touch each other externally at a point P. Find the coordinates of P A. (-3,-2) B.(7/5,4/5) C.(3,2) D.(5,7/2) E.(7,5)
最佳解答:
C: ( x + 1 )2 + ( y + 1 )2 = 25 Centre of C: ( -1 , -1 ) and radius of C = 5 C': ( x - 11 )2 + ( y - 8 )2 = 100 Centre of C': ( 11 , 8 ) and radius of C' = 10 Draw a line passing through both centres ( L ). As the radii are in the ratio of 1 : 2, P is actually a point dividing L in the ratio of 1 : 2, so let P be ( x , y ). x = ( 11 - 2 ) / ( 1 + 2 ) = 3 y = ( 8 - 2 ) / ( 1 + 2 ) = 2 Hence P is ( 3 , 2 ). [ Ans : C ]
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CE 1999 MATHS MC#53發問:
Two circles with equations (x+1)^2 + (y+1)^2=25 and (x-11)^2 + (y-8)^2 =100 touch each other externally at a point P. Find the coordinates of P A. (-3,-2) B.(7/5,4/5) C.(3,2) D.(5,7/2) E.(7,5)
最佳解答:
C: ( x + 1 )2 + ( y + 1 )2 = 25 Centre of C: ( -1 , -1 ) and radius of C = 5 C': ( x - 11 )2 + ( y - 8 )2 = 100 Centre of C': ( 11 , 8 ) and radius of C' = 10 Draw a line passing through both centres ( L ). As the radii are in the ratio of 1 : 2, P is actually a point dividing L in the ratio of 1 : 2, so let P be ( x , y ). x = ( 11 - 2 ) / ( 1 + 2 ) = 3 y = ( 8 - 2 ) / ( 1 + 2 ) = 2 Hence P is ( 3 , 2 ). [ Ans : C ]
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