AP EAMCET · Maths · Straight Lines
\(\mathrm{A}(5,3), \mathrm{B}(3,-2), \mathrm{C}(2,-1)\) are three points. If \(\mathrm{P}\) is a variable point such that the area of the quadrilateral \(\mathrm{PABC}\) is 10 sq. units, then the locus of \(\mathrm{P}\) is
- A \(16 x^2-24 x y+9 y^2-144 x+108 y-76=0\)
- B \(16 x^2-24 x y+9 y^2+144 x-108 y-76=0\)
- C \(16 x^2-24 x y+9 y^2-144 x+108 y+76=0\)
- D \(16 x^2-24 x y+9 y^2+144 x-108 y+76=0\)
Answer & Solution
Correct Answer
(A) \(16 x^2-24 x y+9 y^2-144 x+108 y-76=0\)
Step-by-step Solution
Detailed explanation
Area \( = \frac{1}{2} |(x \cdot 3 - y \cdot 5) + (5 \cdot (-2) - 3 \cdot 3) + (3 \cdot (-1) - (-2) \cdot 2) + (2 \cdot y - (-1) \cdot x)| \) Area \( = \frac{1}{2} |(3x - 5y) + (-10 - 9) + (-3 + 4) + (2y + x)| \) Area \( = \frac{1}{2} |3x - 5y - 19 + 1 + 2y + x| \) Area…
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