二十{〇九九- )年九十七國民中
育收日五十月十年午庚腊夏
1991 中學會考預習專欄
明德出版社
MILL & DALE PRESS
Additional Mathematics (9)
'From (3)
(2) x (4)
邹日僑華
Exercise 9
六期星
日一月二十(〇九九一)年九十七國民華中 (ad
A variable toint P on the parabola 16x, find the locus of the mid- point of the line segnent joining (3, 4) and P
2. The sum of square of distance from a moving point P to the line.xy0 and a point (1), 155 sq. units. Find the locus of P.
31 It is a variable, point on the curve. 5. The feet of perpendicular. from H to the axes are A and B. Find the locus of the mid- coint of AB.
412 = 1612x
16 32% 41-160
2. Let (x, y) be the coordinates of
Square of distance from P tó ene line x › ya 0 is.
Scuore of distance from P to e. Dofnt. (r. 1) is
Dy+34}{ x2-
3x + 3y +6×3y?-32x3-32y3-32×3y-32xy? +120x+120y-32xy = 0
(Ans.)
Let ( be the coordinates of k' be the mid-point of A, By équation of the variable" line. The Coordinates of A is (k + 3, k), the coordinates of P IS (A. 2k, k)" (4-2k)
大埔津中 英文文憑教師
91年二月二日到職,應徵者講親繕 履歷附近電話函大埔富善邨圓玄 學院第二中學校長收或電6616038 鄧小姐洽
沙田津中
英文學位教師
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Revision Exercise 9
Coordinates Geometry 11 - Loci
Worked Example
1. A straight line L which passing through a fixed point (0, 4), cuts the circle xy at two points. P and PP is another point on 1 between
· such. that: PPDB Find the equation of locus of the print P.
Solution
"Let
be the
coordina respec
Put
4y #
Put (5) in (7)
-1
(6)
4. Given three points A(3, 5), (0, or, £15, 3). From a point P, PA, PB and PC are joined, [ PA PB PC, find the locus. of P..
S. Avariable line parallel to the x-axis cuts the curve x = y at
The equation of Tucus of P is
·DE
Fans.
2. Find the locus of a point, such that the mid-point of P and ALT.- lies on the cirule‹ x2 + y2.
Solution:
Let #ix, y) be a paint the locus. Then the midpoint of PA is (*44 244)..
Put the mid-point in the equation
A and the line x + 2y - 40 at B. Find the focus of the mid-point of AB
6. A(30) and R(5, 0) are two fixed points and 0 is the origin. P is a noving point such that OPB is a right angle. find, the equation.or the locus of the mid-point Q OF AN
7. The feet of perpendicular from a moving paint P to the x-axis and y-axis are A and B respectively. If CA OB find the locUE OF P
Solution to Exercise 9
3x2+3y2+2xy=4x+4y-† =10 (Ms.)
3. Let (h, k) be the coordinates of HÒ Then (n. 01, (0,8) are .the coordinates of A and B. respectively. The mid-point of AB is
2y
Th, kt lies on, 2x 2
5
Let ki be the coordinates of
PA PB.
The mid-point of P. and 13, 41s
The locus is e circle (1-1), radius 16.
certre
(Ans.)
4:0 (0)
satisfying
above system
both
the solut
(x-3)
The Coordinates of
(Ans.)
be the
5. Lot
(a, b). coordinates of P.-Q respectively.
شهد
Slope, of ap
Slope of Pi
.5(2x)
22x + 24 =0
(Ans,
7. Let (x, y) be the coordinates of P.
Coordinates uf
coordinates of 8:1s (q, y),
DA • QB = b
•Required equation; xy=
***7*+k=0 has no real foot
10
49-4 CO
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Mathematics (9)
Exercise 9. Inequal
Section A
Solve the inequal
(Ax+3)
Inequales.
(a) Find,
漆
Solve the simultaneous inequalities.
J. Solve the preq
2x + 1
Solve the inequal
HONG
x+2y 18
(b). Hence, find
(i) the marisum value of 2x-y+5 (ii), the minimum value of xt2y+^.
satisfying the inequalities in (a):
Solutions to exercise 9
4. 7(4x-3142 & 3 (2x+3)- —
Multiply both sides by 4
-5(4x-3)+8612x+3)-1 20x-15+8 12x+18:1 8x 24 X 3
3x-9 -2x+2
11
√(x+1) | | 3x+5)
圖
Multiply both sides by 12-
4(x+1). > 3(3x+5)
4x+49x+15
5x11
11
Since there is NO real, number which (a)
is less than
and also greater
.6
OF
than Thus, there is NO SOLUTION- For the given. inequalities.
system
72+19x-3x-
Thus,
́8+3X), 0°
B+3xK
ས་
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田忠孝街 89 號人事主任收
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1509
助教、
急聘
半日代課 54
Solve the inequali
72+ 19x8x* K
Solve the inequality
36x* - 69x * 30->
Section 8
7. Find the range of k such that
(a) the equation x2+7x+k=0
real root,
(b) the equation x-(k+1)x+40
two real roots,
B. (a) Fine, graphically, the soly
of the inequalities.
x + 2y 8
6.
$121 = *+thy #
Multiply both sides by. 3(2x-1)-2(x+1) 25:
6x-3-2x-2 % 5
(1) and (2)
***[Ans:)
The solution for the first system of Inequalities is x 9 and there 75 no solution for the second system of inequalities.
···36x69x+30 >0;
| 3(12x2-23x+10) 2.0
(4x-5)(3x-2) 0.
(Angl
-(k+11x+4ND has two real roots
As shown in
JES
[Ansu
Figura the points
sets of x, given system
in the pace agion (including the
LIBRA
AONG PUBLIC
(b) Hence, ing the maximum
the
expression
1991中學會考預習專欄
3x+6
is always true.
Economic & Public Affair
Thus,
The points satisfying the given inequalities are the dots marked ig - the above graph. (Note: (2, 0), 14, 7) and (6, 6) are not included as x+2y18) (b).
The maximun value of 2x-y satisfying the inequalities in (al
2021
The required maximum value
of
maximum constraints given in (a) when
under
the
of x12y
the inequalities in
X=4 and 2.
(a)
Maximum value of 2x+3y is
2.4-2(2)
214)+3(21 14.
Maximum value of -2x+3y+10- Satisfying
The required minimum value
(Ans.)
the inequalities is 14. + 10,
Company
each partner has limited power
each partner shares som duties
accounting
Tawyer
unlimited and may be perpetual
shares are
transferable
Shareholders contrul through the Board of Directors
salaried managers
factories
Hong Kong Telephone Company Limited
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Business limits (3)
Comparist
Types of
ownership
Compare
急聘會計
1. Ease of formation
̇九龍某校
2. Cost of formation
little cost
誠聘會計
Sole Proprietorship
very easy and few Tegal procedures
little cost
Partnership
easy but have to draw an article of partnership
difficult and a lot of legal procedures. needed!
high cost because of incorporation, and legal fees
Types of
ownership
Solà Proprietorship
Compate
'1. Kwok
12. Continuity;
limited and based on health of the owner.
13. Transfer of
Ownership
at will of the owner-
limited
14. Control of the firm
Limited. Company
the owner has full. power
15. Owner(s) and
anager(s)
owner manager.
16, Common examples
Barber shop
3. Personal incentive
of owner(s)
very high
Tow
有意者請電三八六三一四九治
Credit standing
"lowest
-nigh
5. Liability of
owner(s).
unlimited liability
unlimited liability
limited liability
Types of
limited
company
Private limited company
6. Size
sma}}
誠聘學位教師
7. Opportunity for
larger
possible
unlimited size
possible.
Cumpare
No. of shareholders.
employees to be
九龍城區中學誠聘各科學位教 師多名,有意請繕體歷相片寄 本報信箱1149號。
prijsoted as owner(s).
8. Managerial
efficiency
9. Freedom of action
10. Promptness of action
11. Ease of dissolution
inforio
immediate
very easy
very free
better because of division, of labour Among partners
some limitation
slower
high
such himitation:
slorest
0a5y
difficult and have to Follow Tegal procedures
Public limited company
No. of directors
Iranster of ownership
Secrecy
Fundraising
Capital requirement
12.00 50
1
privately transferred
not required to publish accounts on the, pross
mainly by existing shareholders
-Sea Her
2 to unligited
at least 2
in stock exchange market
required to publish operation results on the press.
inviting public to buy shares
Färger
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