Q. 54.0( 4 Votes )

# The straight line through P(x_{1}, y_{1}) inclined at an angle θ with the x–axis meets the line ax + by + c = 0 in Q. Find the length of PQ.

Answer :

**Given:** the equation of the line that passes through P(x_{1}, y_{1}) 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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