1. P is the point(7,5). Q and R are points on the line L: x+2y=6 such that PQ=PR=5, find the equation of a line passing through the mid-point of QR and parallel to the line 5x-2y=2.
2. A is a point (-3,-1) and B is the point (-1,1). AB is produced to a point C such that AC=3AB. Find the coordinates of C.
3. If the two straight lines L1: ax+by-6=0 and L2:5x+4y-16=0 does not intersect and L1 passes the point [ a, (-2a+1)/2 ], find the values of a and b.
4. It is given that a fraction is in the form (p/q), where p,q are positive integers. The denominator of the fraction is greater than the numerator by 3. When both the numerator and denominator are increased by 2, the value of the fraction is doubled. Find the fraction.
5. The simultaneous equations y=x^2+m and y=-2x+1 have real solutions. Find the range of values of m.
Thank you.
F.4 maths
2010-03-09 5:56 am
回答 (2)
2010-03-14 6:03 am
無最佳解答
2010-03-09 10:48 pm
1.
let S(s,(6-s)/2) is a point on L
when PS=5
(7-s)^2+(5-(6-s)/2)^2=25
49-14s+s^2+25-5(6-s)+(6-s)^2/4=25
5s^2/4-12s+28=0
5s^2-48s+112=0
s=28/5 or 4
Q and R =(28/5,1/5) and (4,1)
mid point of Q and R=(24/5,3/5)
the required equation is (y-3/5)/(x-24/5)=5/2 ie 25x-10y-114=0
2.
let C=(a,b)
AC=3AB
So,AB:BC=1:2
-1=(a+(-3)(2))/(1+2)
a=3
1=(b+(2)(-1))/(1+2)
b=5
C=(3,5)
2010-03-09 15:00:33 補充：
3.
L1 and L2 does not intersect
so, L1 and L2 are parallel
-a/b=-5/4
b=4a/5
ax+by-6=0
a^2+(4a/5)(-2a+1)/2-6=0
a^2+2a-30=0
a=-1+(31)^0.5 or -1-(31)^0.5
b=4(-1+(31)^0.5)/5 or 4(-1-(31)^0.5)/5
2010-03-09 15:04:37 補充：
4.
p+3=q
(p+2)/(q+2)=2p/q
so,
(p+2)/(p+5)=2p/(p+3)
p^2+5p-6=0
p=1 or -6(rejected)
q=4
the fraction is 1/4
2010-03-09 15:07:26 補充：
5.
y=x^2+m and y=-2x+1
x^2+2x+(m-1)=0
(2)^2-4(1)(m-1)=>0
m<=2
let S(s,(6-s)/2) is a point on L
when PS=5
(7-s)^2+(5-(6-s)/2)^2=25
49-14s+s^2+25-5(6-s)+(6-s)^2/4=25
5s^2/4-12s+28=0
5s^2-48s+112=0
s=28/5 or 4
Q and R =(28/5,1/5) and (4,1)
mid point of Q and R=(24/5,3/5)
the required equation is (y-3/5)/(x-24/5)=5/2 ie 25x-10y-114=0
2.
let C=(a,b)
AC=3AB
So,AB:BC=1:2
-1=(a+(-3)(2))/(1+2)
a=3
1=(b+(2)(-1))/(1+2)
b=5
C=(3,5)
2010-03-09 15:00:33 補充：
3.
L1 and L2 does not intersect
so, L1 and L2 are parallel
-a/b=-5/4
b=4a/5
ax+by-6=0
a^2+(4a/5)(-2a+1)/2-6=0
a^2+2a-30=0
a=-1+(31)^0.5 or -1-(31)^0.5
b=4(-1+(31)^0.5)/5 or 4(-1-(31)^0.5)/5
2010-03-09 15:04:37 補充：
4.
p+3=q
(p+2)/(q+2)=2p/q
so,
(p+2)/(p+5)=2p/(p+3)
p^2+5p-6=0
p=1 or -6(rejected)
q=4
the fraction is 1/4
2010-03-09 15:07:26 補充：
5.
y=x^2+m and y=-2x+1
x^2+2x+(m-1)=0
(2)^2-4(1)(m-1)=>0
m<=2
收錄日期: 2021-04-13 17:08:59
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