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.

Question

Philoid · Accepted 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