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Find the equation of the line passing through the intersection of lines x-3y+1=0,2x+5y-9=0 and whose distance from the organ 2.23

Find the equation of the line passing through the intersection of lines x-3y+1=0,2x+5y-9=0 and whose distance from the organ 2.23

Grade:11

1 Answers

Aryan Vartak
24 Points
6 years ago
Say x – 3y + 1 = 0  ----(1) 
&   2x + 5y – 9 = 0  ----(2)
 
By using intersection formula and solving for both x & y from (1) & (2), we get;
x = 2        y = 1
 
Now, by using the equation
 (y-y_{1}) = \frac{(y_{2} - y_{1})}{(x_{2} -x_{1})} (x - x_{1})        placing (x1, y1) = (0, 0)
                                                                                   (x2, y2) = (2, 1)
We get 
y = \frac{1}{2} x
 
Multiplying both sides by 2, we get
x - 2y = 0

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