Question

Find the centroid of the region that is bounded below by the x-axis and above by the ellipse 1. Question 1 What are the coordinates of the centroid? (Simplify your answers. Round to four decimal places as needed.) Match the equation with the graph. Include the directrix that corresponds to the focus at the origin. Label the vertices with appropriate polar coordinates. If the equation is an ellipse, label the center as well. 910 35 + 7 sino Question 2 re Choose the correct graph below. A. ОВ. OC. OD. 140 140 - 140 - 140 -140 Find the polar coordinates of significant points on the graph. Select the correct choice below and fill in the answer boxes to complete your choice. (Type ordered pairs. Type exact answers, using a as needed. Use angle measures greater than or equal to 0 and less than 2t. Use a comma to separate answers as needed.) O A. The graph is a parabola. The polar coordinates for the vertex are OB. The graph is an ellipse. The polar coordinates for the vertices are The polar coordinates for the center are

Answer 1

Solution 2. 1) Giveni 2 Since it is symmetric about yo axis below x-axis So, Co-ordinate of centroid in in y-axis i e : 0 And y Syd SIA g2 dae Jy dx s 911- (-). Sosi 2x ge2 dx 4 Ia

2 I, 9. x. lx -2 2. 9 - 3 4 -2 - 9(2+2) = zº+2) 4 36-12 I, = 24 & Iq y d x - 2 dx 2 2 ms. 2 2 4 Sint I ja = x² 3 (28="() - 2 5*(-] 2. 3 TT 2. T २ = 3T Hence, 네 Ii 24 Iz 3T And, Centroid 0

2) Given i 35+ 7 Sino So, x(0,0) = 8 Cose 9 10 Coso 35+7 Sino and, y (ro) = 8 Sino 9 10 Sino 35+7 Sino ac 2 ty Sgain, (3 35 7 Sino) = 910 358 +78 Sino = 910 =) 355x² + y2 + 7 y = 910 910-74 35 2 (26 - 5") 2 =676+ 25 ge? + BG yaşay = 676 = 676 *2 (9-2, (y + 1039403 (3-6 ay + 676 + 169 G 25 202 + ५२२5/6 Hence, 105625/144 ellipose, whose graph it

105625 Tuy follows. Major axis ago axis & Minor anisa x-anis, YR25 6 And centre 65 Hence similar to option 'A graph is the 3) Polar Coordinate of significant points graph is x (O) = 8 Coso 9,0 coso 35+7 Sino A y (0) & Sino 910 Sino 35+7 Sino T/4/2 3/4 S1/4 3/7/4 26 116.12 1-16.11 0 21.41 -26 -21.41 16.12 21:67 16.11 1-21.41-32.5 -21.41 Centre of the ellipse (0, -32.5)