AP EAMCET · Maths · Straight Lines
If \(A=(2,3)\) and \(B=(-4,5)\) are two fixed points, then the locus of a point \(P\) such that the area of \(\triangle P A B\) is 12 square units is
- A \(x^2+6 x y+9 y^2+22 x+66 y+23=0\)
- B \(x^2-6 x y+9 y^2+22 x+66 y+23=0\)
- C \(x^2+6 x y+9 y^2-22 x-66 y-23=0\)
- D \(x^2-6 x y+9 y^2-22 x-66 y-23=0\)
Answer & Solution
Correct Answer
(C) \(x^2+6 x y+9 y^2-22 x-66 y-23=0\)
Step-by-step Solution
Detailed explanation
Let the co-ordinate of the point \(P\) is \(\left(x_1, y_1\right)\). Then, the area of the triangle \(=12\) \(\Rightarrow \frac{1}{2}\left|\begin{array}{ccc}2 & 3 & 1 \\ -4 & 5 & 1 \\ x_1 & y_1 & 1\end{array}\right|=12\)…
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