Q5 of 319 Page 24

The straight line through P(x1, y1) inclined at an angle θ with the x–axis meets the line ax + by + c = 0 in Q. Find the length of PQ.

Given: the equation of the line that passes through P(x1, y1) and makes an angle of θ with the x–axis.

To find:


Length of PQ.


Explanation:



Let PQ = r
Then, the coordinates of Q are given by


Formula Used:


⇒


Thus, the coordinates of Q are


Clearly, Q lies on the line ax + by + c = 0.


∴


⇒ r


∴ PQ


Thus, length PQ


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