Q2 of 319 Page 24

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.

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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