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AP EAMCET · Maths · Straight Lines

The points on the straight line \(3 x-4 y+1=0\) which are at a distance of 5 units from the point \((3,2)\) are

  1. A \(\left(-2,-\frac{7}{4}\right),\left(-3, \frac{-5}{2}\right)\)
  2. B \(\left(4, \frac{11}{4}\right),(-1,-1)\)
  3. C \(\left(1, \frac{1}{2}\right),\left(2, \frac{5}{4}\right)\)
  4. D \((7,5),(-1,-1)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \((7,5),(-1,-1)\)

Step-by-step Solution

Detailed explanation

Let the point \(A(x, y)\) on the line \(3 x-4 y+1\) is at distance 5 units from the point \((3,2)\). \(\frac{x_1-3}{\cos \theta}=\frac{y_1-2}{\sin \theta}= \pm 5\) \(\Rightarrow \quad x_1=3 \pm 5 \cos \theta\) ...(i) \(y_1=2 \pm 5 \sin \theta\) ...(ii) Since,…