Question

All

1. Consider the parabola 2 - 6x +10y - 1 = 0. () Find the vertex, focus, directrix, and axis of symmetry of the parabola. (b) Sketch the graph of the parabola. 2. Consider the ellipse 9x2 + 25y2 + 361 - 150y +36 = 0. (a) Find the center, vertices and foci of the ellipse. (b) Sketch the graph of the parabola. (b) Sketch the graph of the hyperbola. 3. Consider the hyperbola r? - 4y? +43 + 8y - 40. (a) Find the center, vertices, foci, and asymptotes of the hyperbola.

Answer 1

+) 22 - 6x Hoy-1=0 a) 22 - 6x +10y-1 = 0 sa x2 2x3x + +10y - LED = (x - 3)' +log -10 20 log = =(x-172470. 5 g = + (x-3)?+| Use the vertex form y=aa -b ² tk azt, h = 3, k= Vertex (hik) = (3, 4). distance from the verter to a foers is to qa را دور ) Focus = Ch, ktp) =(3, 15/2) - (31-32

=>(37+0)2+(sy=1952 - 225 5 (31+0), ssy 1)2 = 225 3 962+2)2 + 25 (y - 3)2 225 -) @ +232 + (y - 3) 2 9 Vertex (hik)= (-2,3) Center (hik) = (-2,3) vertices (htaik) - (-275, 3) -(-7,3), (3,3) Foci : (htc,k) ca2b² = Sesa

Center (hik) = (-2, 1) - a2 +62 = t t - s. Ventices: (cht aik) - (- 2 + 2 !). = (0,1), (-4,1) Faci: (htrik) = (-22 55,1) - (+2+JS, D) (-2-58,1) Asymptotes : y = 2 + 2 y = -2 b) Graph