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AP EAMCET · Maths · Straight Lines

The locus of the point \(P\) such that the area of the \(\triangle \mathrm{PAB}\) is 7 , where \(\mathrm{A}(4,5)\) and \(\mathrm{B}(-2,3)\) are given points, is

  1. A a straight line
  2. B a pair of parallel lines
  3. C a circle
  4. D an ellipse
Verified Solution

Answer & Solution

Correct Answer

(B) a pair of parallel lines

Step-by-step Solution

Detailed explanation

\( \text{Area} = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| \) \( 7 = \frac{1}{2} |x(5 - 3) + 4(3 - y) + (-2)(y - 5)| \) \( 14 = |2x + 12 - 4y - 2y + 10| \) \( 14 = |2x - 6y + 22| \) \( 2x - 6y + 22 = 14 \quad \text{or} \quad 2x - 6y + 22 = -14 \)…