# 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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