On the coordinate plane, there is a figure $\Gamma$ with equation $(x-1)^2 + (y-1)^2 = 101$. Select the correct options. (1) $\Gamma$ intersects the negative $x$-axis and negative $y$-axis at $(-9, 0)$ and $(0, -9)$ respectively (2) The point on $\Gamma$ with the maximum $x$-coordinate is $(11, 0)$ (3) The maximum distance from a point on $\Gamma$ to the origin is $\sqrt{2} + \sqrt{101}$ (4) Points on $\Gamma$ in the third quadrant can be expressed in polar coordinates as $[9, \theta]$, where $\pi < \theta < \frac{3}{2}\pi$ (5) After a rotational linear transformation, the figure can still be expressed by a quadratic equation in two variables without an $xy$ term
On the coordinate plane, there is a figure $\Gamma$ with equation $(x-1)^2 + (y-1)^2 = 101$. Select the correct options.\\
(1) $\Gamma$ intersects the negative $x$-axis and negative $y$-axis at $(-9, 0)$ and $(0, -9)$ respectively\\
(2) The point on $\Gamma$ with the maximum $x$-coordinate is $(11, 0)$\\
(3) The maximum distance from a point on $\Gamma$ to the origin is $\sqrt{2} + \sqrt{101}$\\
(4) Points on $\Gamma$ in the third quadrant can be expressed in polar coordinates as $[9, \theta]$, where $\pi < \theta < \frac{3}{2}\pi$\\
(5) After a rotational linear transformation, the figure can still be expressed by a quadratic equation in two variables without an $xy$ term