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
- A a straight line
- B a pair of parallel lines
- C a circle
- D an ellipse
Answer & Solution
Correct Answer
(B) a pair of parallel lines
Step-by-step Solution
Detailed explanation
\( \text{Area} = \frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)| \) \( 7 = \frac{1}{2} |x(5 - 3) + 4(3 - y) + (-2)(y - 5)| \) \( 14 = |2x + 12 - 4y - 2y + 10| \) \( 14 = |2x - 6y + 22| \) \( 2x - 6y + 22 = 14 \quad \text{or} \quad 2x - 6y + 22 = -14 \)…
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