Express the following polar coordinates (r, 0) with corresponding Cartesian coordinates (x, y (expressed in the simplest radical) (a) (2, - 47 ) = (-a, vb) (b) ( 1, 8 ) = ( 2, ; ) ( c) ( 3 , 3x ) = ( - ah, 247 ) Fill in a to I with positive integers a b , d = e g h 2 J = kSuppose that the plane E contains the line L : $41 y-6 2+1 2 3 6 and is perpendicular to the plane x - 3y + 3z + 4 = 0. Which of the following statements about the plane E and n, a normal vector of E, is true? (a) n is parallel to (2, 3, -6) x (1, -3, 3) and E contains the point (1, -6, 1) (b) n is parallel to (2, 3, -6) x (1, -3, 3) and E contains the point (-1, 6, -1) (c) n is parallel to(-, 2, -2 ) x (1, -3, 3) and E contains the point (1, -6, 1) (d) n is parallel to( 7, 3' 2, -- ) x (1, -3, 3) and E contains the point ( -1, 6, -1) O (a) O (b) O (c) O (d)Suppose that the vector n = (1, -2, 1) is perpendicular to a plane E and P( -1, 2, 4) E E. Find an equation of E (a) (2 - 1) - 2(y + 2) + (z+ 4)=0 (b) ( 2 + 1) - 2(y - 2) + ( 2 - 4) =0 (c) - (2+ 1) + 2(y - 2) +4(2 + 1) =0 (d) - (2 - 1) + 2(y + 2) +4(2 - 1) =0 O (a) O (b) O (c) O (d)Determine the graphs of the following equations. (ellipse, parabola or hyperbola) (a)ac2 + 2(y - 1)2 = 4: [1=4 ] (b)ac - yz = 1: [ME ] V (c ) - (2+ 2) 2 + 592 = 1: [ MEH ] V 4On which of the following intervals is f(a) - -23 + 4x2 - 5xc + 2 greater than or equal to zero? (Note. There might be multiple answers.) (a) [0, 1] (b) [1, 2] (c) [2, 3] (d) [3, 4] (a) O (b) O (c) O (d)