Q. 104.8( 5 Votes )

Find the equations of the lines through the point of intersection of the lines x – 3y + 1 = 0 and 2x + 5y – 9 = 0 and whose distance from the origin is.

Answer :

Given:


Lines x – 3y + 1 = 0 and 2x + 5y – 9 = 0


To find:


The equations of the lines through the point of intersection of the lines x – 3y + 1 = 0 and 2x + 5y – 9 = 0 and whose distance from the origin is.


Explanation:


The equation of the straight line passing through the point of intersection of x 3y + 1 = 0 and 2x + 5y 9 = 0 is given below:


x 3y + 1 + λ(2x + 5y 9) = 0


(1 + 2λ)x + ( 3 + 5λ)y + 1 9λ = 0 … (1)


The distance of this line from the origin is



1 + 81λ2 – 18λ = 145λ2 – 130λ + 50


64λ2 – 112λ + 49 = 0


(8λ – 7)2 = 0


λ


Substituting the value of λ in (1), we get the equation of the required line.



22x + 11y – 55 = 0


2x + y – 5 = 0


Hence, equation of required line is 2x + y – 5 = 0.


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