If A=(-1, 2) and B=(1, -2) are two points and | vedclass

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(A) Let the coordinates of point $P$ be $(x, y)$.Given that the area of $	riangle PAB = 1$.The area of a triangle with vertices $(x_1, y_1), (x_2, y_

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$4x^2 + 4xy + y^2 = 1$

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(A) Let the coordinates of point $P$ be $(x, y)$.Given that the area of $	riangle PAB = 1$.The area of a triangle with vertices $(x_1, y_1), (x_2, y_2), (x_3, y_3)$ is given by $\frac{1}{2} |x_1(y_2 - y_3) + x_2(y_3 - y_1) + x_3(y_1 - y_2)|$.Substituting the coordinates $P(x, y), A(-1, 2), B(1, -2)$:$	ext{Area} = \frac{1}{2} |x(2 - (-2)) + (-1)(-2 - y) + 1(y - 2)| = 1$$\frac{1}{2} |x(4) + (2 + y) + (y - 2)| = 1$$\frac{1}{2} |4x + 2y| = 1$$|2x + y| = 1$Squaring both sides:$(2x + y)^2 = 1^2$$4x^2 + 4xy + y^2 = 1$.

If $A=(-1, 2)$ and $B=(1, -2)$ are two points and $P$ is a variable point such that the area of $\triangle PAB$ is always $1$,then the equation of the locus of $P$ is

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