find the equation of the straight line joining the point of intersection of 3x+y+2=0 and x-2y-4= to the point of intersection of 7x-3y=-12 and 2y=x+3
Answers
Answer:Step 1.
( Finding the point of intersection of the first pair of lines )
The first pair of straight lines are
3x + y + 2 = 0 .....(1)
x - 2y - 4 = 0 .....(2)
Multiplying (1) no. equation by 2 and adding with (2) no. equation, we get
6x + 2y + 4 + x - 2y - 4 = 0
⇒ 7x = 0
⇒ x = 0
Putting x = 0 in (1) no. equation, we get
0 + y + 2 = 0
⇒ y = - 2
∴ (0, - 2) is the point of intersection of the first pair of straight lines.
Step 2.
( Finding the point of intersection of the second pair of lines )
The second pair of straight lines are
7x - 3y = - 12 .....(iii)
2y = x + 3 ⇒ x = 2y - 3 .....(iv)
Using (iv), from (iii), we get
7 (2y - 3) - 3y = - 12
⇒ 14y - 21 - 3y = - 12
⇒ 11y = 21 - 12 = 9
⇒ y = 9/11
Putting y = 9/11 in (iv) no. equation, we get
x = 2 (9/11) - 3
⇒ x = 18/11 - 3
⇒ x = (18 - 33)/11
⇒ x = - 15/11
∴ (- 15/11, 9/11) is the point of intersection of the second pair of straight lines.
Step 3.
( Finding the required line of intersection )
The two points of intersection are (0, - 2) and (- 15/11, 9/11).
Thus, the line passing through the above points is
(x - 0)/{0 - (- 15/11)} = {y - (- 2)}/(- 2 - 9/11)
⇒ x/(15/11) = (y + 2)/{(- 22- 9)/11}
⇒ 11x/15 = (y + 2)/(- 31/11)
⇒ 11x/15 = - 11 (y + 2)/31
⇒ 31 * 11x = - 15 * 11 (y + 2)
⇒ 341x = - 165y - 330
⇒ 341x + 165y + 330 = 0 (Ans.)
Step-by-step explanation:
Answer:
here's ur answer dude
Step-by-step explanation:
Line passing through point of intersecting of L
1
,L
2
is given by L
1
+λ
2
=0
⇒(3x+2y+4)+λ(2x+5y−1)=0
⇒x(3+2λ)+y(2+5λ)+4−λ=0
Distance of (2,−1) to this line,
∣
∣
∣
∣
∣
∣
(3+2λ)
2
+(2+5λ)
2
2(3+2λ)−(2+5λ)+4−λ
∣
∣
∣
∣
∣
∣
=2
⇒6+4λ−2−5λ=2
29λ
2
+32λ+13
⇒−2λ+8=2
29λ
2
+32λ+13
⇒λ
2
+16−8d=29λ
2
+32λ+13
⇒28λ
2
+40λ−3=0⇒28λ
2
+42λ−2λ−3=0
14λ(2λ+3)−(2λ+3)=0
(14λ−1)(2λ+3)=0⇒λ=
14
1
or λ=
2
−3
L:x(3+
7
1
)+y(2+
14
5
)+4−
14
1
=0
44x+33y+55=0⇒
4x+3y+5=0
or x(3−3)+y(2−
2
15
)+4+
2
3
=0
⇒y(−11)+11=0⇒
y=1