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41.
Let
f(x,y) = x² + y² - 2x - 4y - 95
g(x,y) = 25x² + 25y² - 370x - 340y + 225

Sub (9,8), (7,10), (-5,10), (-7,-4) into f(x,y) and g(x,y) respectively
Only f(9,8) = g(9,8) = 0

∴ A. (9,8)

42.
O(0,0)　　　P(-40,20)　　　Q(40,20)
PQ is a horizontal line and the mid-pt of PQ = (0,20) , then the x-coordinates of the circumcentre = 0
Let a be the y-coordinates of the circumcentre
The mid-pt of Q and O = (20,10)
[(a - 10)/(0 - 20)] [(20 - 0)/(40 - 0)] = -1
a - 10 = 40
a = 50

∴ D. 50

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43.
P(can hit the target) = 6/7　　　　　　P(cannot hit the target) = 1/7
P(at least hit the target twice) = 1 - (1/7)⁵ - 5×(6/7)(1/7)⁴ = 16776/16807
P(only hit the target three times) = C(5,3) (6/7)³ (1/7)² = 2160/16807
Probability
= P(only hit the target three times) / P(at least hit the target twice)
= 2160/16776
= 30/233

∴ D. 30/233