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CHAPTEB CHAPTER 8 ANALYTIC GEOMETRY 8 PRACTICE TEST ) For the following exercises, write the equation in standard form and state the center, vertices, and foci

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CHAPTEB CHAPTER 8 ANALYTIC GEOMETRY 8 PRACTICE TEST ) For the following exercises, write the equation in standard form and state the center, vertices, and foci. r.t+'-=r g 4 9t' + t6x, _ Z, 36y + 32x g2_O For the following exercises, sketch the graph, identifying the center, vertices, and foci. - (x-3)' (v- 5' 2tt write the standard form eguation ofan ellipse with center at ( I, 2 ), vertex at (7' 2), and focus at (4, 2). a 6. A whispering gallery is to be constructed with a tengtrr of tso feet. ti the foci are to be located 20 feet away from the wall, how high should the ceiling be? For the follorving exercises, write the equation of the hyperbola in standard form, and give the center, yertices, foci, and asymptotes. x2 t'l 49 8t 8. 16.}. - 9xr ! 12q, + I12 = 0 For the following exercises, graph the hyperbola, noting its center, vertices, and foci. State the e quations of the asymptotes. s.(x-3)'_(y+31'z_l 25 11. 10. I y' x'z+ 4y ,lx - 18:0 Write the standard form equation ofa hlperbola with foci at ( I, 0) and ( l, 6), and a vertex at (1, 2). For the following exercises, write the equation of the parabola in standard form, and give the vertex, focus, and equation of the directrix. 12. f + llx- 0 13.3x, - tzx _ y + 1t:O For the follorving exercises, graph the parabola, labeling the vertex, focus, and directrix. 14.(x16' 1)r- a0+ 3) r5.y.+8x_ 8/+40_0 write the equation ofa parabora with (2, 3) and directrix 7 : - l. a focus at 17. A searchright is shaped like a paraboloid of revolution. Ifthe light source is located 1.5 feet from the base along the axis of symmetry, and the depth ofthe searchlight is 3 feet, what should the width of the opening be? For the following exercises, determine which conic section is represented by the given equation, and then determine the angle I that will eliminate the xy term. 18,3x' - 2xy + 3Y :4 19. x, + 4xy + For the following exercises, rewrite in the -ri'system without the tx]+tO\/1xy+y.:4 bl + 6r - 81: Q .ri'term, and graph the rotated graph 21, 16x'z + 244r + 9f - t25x = O or the following exercises, identify the conic with focus at the origin, and then give the directrix and eccentricity. 22. 2-sind 4+ 6cosj For the following exercises, graph the giyen conic section. an ellipse or a hyperbola, label vertices and foci. 24- r: 12 4 gsing Ifit is a parabola, label vertex, focus, and directrix. 2 25'l:4+4sino 25. Find a polar equation of the conic with focus at the origin, eccentricity ofe 2, and directrix: 3. : x: Download for free at http://cnx.org/contonts/9bo8c2g4_057t4201'9t4a-5d6a.lgg274oda)s 5t Ifit is