Q1. The coordinates of the centre of the circle C are (4, 6). It is given that the
horizontal line y=1 is a tangent to C.
(a) Find the equation of C. 我知道這條是這樣做: (x- 4)^2 + (y- 6)^2 = 5^2
x^2 + y^2 - 8x- 12y +27= 0
(b) L is a straight line with slope -1/2 and x-intercept k. L cuts C at A and
B. Express the mid-point of A and B in terms of k. 我不知道這條如何做,可否列式。
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我不知道這條如何做,可否列式。
Q2. In the beginning of 2011, Penny bought a cat. Her cat ate 30 cans of food
every month in the first year. In the beginning of every succeding year, her cat
requires 5 more cans of food every month than the previous year.
(a) How many cans of food does she buy in n years? (Assume the life of the
cat is longer than n years.)
(b) Penny wants to buy one more cat in the beginning of 2014. She expects that the new cat eats 20 cans of food every month in the first year and 3 more cans
every month than the previous year. She wants to find the budget on feeding the cats. If the cost of a can of food is $15, and she assumes that the cats will not
die before the end of 2020 and the costs of food wil not change, how much will
she spend on feeding the two cats from the beginning of 2011 to the end of
2020?