Q. 14.0( 6 Votes )
Find the equation of a straight line through the point of intersection of the lines 4x – 3y = 0 and 2x – 5y + 3 = 0 and parallel to 4x + 5 y + 6 = 0.
Answer :
Given:
Lines 4x – 3y = 0 and 2x – 5y + 3 = 0 and parallel to 4x + 5 y + 6 = 0
To find:
The equation of a straight line through the point of intersection of the lines
Explanation:
The equation of the straight line passing through the points of intersection of 4x − 3y = 0 and 2x − 5y + 3 = 0 is given below:
4x − 3y + λ (2x − 5y + 3) = 0
⇒ (4 + 2λ)x + (− 3 − 5λ)y + 3λ = 0
⇒ y
The required line is parallel to 4x + 5y + 6 = 0 or, y
∴ 
⇒ λ 
Hence, the required equation is
⇒ 28x + 35y – 48 = 0
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