Q. 24.3( 3 Votes )
If the straight line through the point P(3, 4) makes an angle 
with the x–axis and meets the line 12x + 5y + 10 = 0 at Q, find the length PQ.
Answer :
Given: (x1,y1) = A(3, 4), θ = 
30°
To find:
Length PQ.
Explanation:
So, the equation of the line is
Formula Used: 
⇒ 
⇒ 
⇒ x – √3 y + 4√3 – 3 = 0
Let PQ = r
Then, the coordinate of Q are given by
⇒ x 
, y 
The coordinate of point Q is 
Clearly, Q lies on the line 12x + 5y + 10 = 0
⇒ 
⇒ r 
PQ = |r| 
Hence, the length of PQ is 
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