gaokao 2020 Q22

gaokao · China · national-III-arts 10 marks Polar coordinates
[Elective 4-4: Coordinate Systems and Parametric Equations] In the rectangular coordinate system $x O y$, the parametric equation of curve $C$ is $\left\{ \begin{array} { l } x = 2 - t - t ^ { 2 } , \\ y = 2 - 3 t + t ^ { 2 } \end{array} ( t \right.$ is a parameter and $t \neq 1 )$. $C$ intersects the coordinate axes at points $A , B$.
(1) Find $| A B |$;
(2) With the origin as the pole and the positive $x$-axis as the polar axis, establish a polar coordinate system and find the polar equation of line $A B$ .
[Elective 4-4: Coordinate Systems and Parametric Equations]\\
In the rectangular coordinate system $x O y$, the parametric equation of curve $C$ is $\left\{ \begin{array} { l } x = 2 - t - t ^ { 2 } , \\ y = 2 - 3 t + t ^ { 2 } \end{array} ( t \right.$ is a parameter and $t \neq 1 )$. $C$ intersects the coordinate axes at points $A , B$.\\
(1) Find $| A B |$;\\
(2) With the origin as the pole and the positive $x$-axis as the polar axis, establish a polar coordinate system and find the polar equation of line $A B$ .