(2+5k)x-(3+4k)y-7k=0...(*) is a familt of st. line passing through a fixed point P, where k is a real number
a.Find the coordinates of P
b.A straight line passes through P but it can't be represented by(*) for any real number k. Write down the equation of this st. line
c.Find the equation of the st. line in the family of(*)with slope3/4
Another family of st. lines is given by equation 4x+3y+c=0...(**) where c is a real number.
d.What is the relation of the st. lines in the family of (**)
e.The area of a striangle formed by a-axis, the line in(c) and the one line in
the family of(**) is 4/3sq units.Find the two possible equation of the lines in the family of(**)
f.What kinds of triangles are formed in(e)
Equations of straight lines
2008-05-26 5:56 am
回答 (2)
2008-05-26 6:22 am
✔ 最佳答案
a. (*) can be written as 2x-3y+k(5x-4y-7)=0∴2x-3y=0------(1)
5x-4y-7=0--------(2)
(1)*5/2
5x=15/2y------(3)
Sub(3)in (2)
7/2y=7
y=2
x=3
∴P=(3,2)
b.The equation of the st. line=5x-4y-7=0
c.Slope of (*)=(2+5k)/(3+4k)
∴(2+5k)/(3+4k)=3/4
8+20k=9+12k
k=1/8
∴The required equation is (21/8)x-(7/2)y-7/8=0
i.e. 21x-28y-7=0
d. The lines in (**) are parallel to each other
e.Slope of line in c=3/4, and slope of line for (**)=-4/3
∴They are perpenducular to each other.
Let the intercept point of the two line are (a,b), where (a,b) satisify both equation
Sub y=0 on 21x-28y+7=0
x=1/3
Sub y=0 in 4x+3y+c=0
x=-c/4
∴sqrt[(1/3-a)²+(0-b)²]*sqrt[(-c/4-a)²+(0-b)²]=8/3
[(1/3-a)²+b²][(-c/4-a)²+b²]=8/3
f. Right-angled triangle.
2008-05-26 6:59 am
c (2+5k)/(3+4k)=3/4
8+2k=9+12k
10k=-1
k=-1/10
EQ of * 1.5x-2.6y+7/10=0
15x-26y+7=0
d they are all parallel
8+2k=9+12k
10k=-1
k=-1/10
EQ of * 1.5x-2.6y+7/10=0
15x-26y+7=0
d they are all parallel
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