The equation of the circumcircle of the quadr | vedclass

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(B) The lines $x = a, x = 2a, y = -a, y = a$ form a rectangle with vertices at $(a, -a), (2a, -a), (2a, a),$ and $(a, a)$.Since the quadrilateral is a

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$x^2 + y^2 - 3ax + a^2 = 0$

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(B) The lines $x = a, x = 2a, y = -a, y = a$ form a rectangle with vertices at $(a, -a), (2a, -a), (2a, a),$ and $(a, a)$.Since the quadrilateral is a rectangle,its circumcircle has the diagonal as its diameter.Taking the diagonal connecting $(a, -a)$ and $(2a, a)$,the equation of the circle is given by $(x - x_1)(x - x_2) + (y - y_1)(y - y_2) = 0$.Substituting the coordinates: $(x - a)(x - 2a) + (y - (-a))(y - a) = 0$.Expanding this: $(x^2 - 3ax + 2a^2) + (y + a)(y - a) = 0$.$(x^2 - 3ax + 2a^2) + (y^2 - a^2) = 0$.$x^2 + y^2 - 3ax + a^2 = 0$.

The equation of the circumcircle of the quadrilateral formed by the lines $x = a, x = 2a, y = -a, y = a$ is:

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