<p>Circles and Parabolas</p><p>Q: Write the equation of the circle that passes through (-1, 3) and has its center at (2, 4).</p><p>Q: Write the standard form of the equation of the parabola whose directrix is y = -4 and whose focus is (2, 2).</p><p>Q: Given y2 - 12 - 16x - 4y = 0 find: a) vertex b) directrix c) axis of symmetry d) focus e) then sketch a graph</p><p>Hyperbolas and Ellipses</p><p>Q: Identify the conic represented by 9y2 + 4x2 - 108y + 24x = -144. State its center, vertices, and axes.</p><p>Q: Consider the hyperbola 12x2 + 24x - 12y2 + 48y = 48. a) find the coordinates of the vertices b) write the equations of its asymptotes c) find the coordinates of the foci d) sketch the graph</p><p>Q: Write the standard form of the equation of the ellipse with foci at (ұ4,0) and whose minor radius is 5 units long.</p><p>Q: Write the standard form of the equation of the hyperbola for which a = 2 if the transverse axis is vertical and the equations of the asymptotes are y = ұ2x.</p><p>Eccentricity 5 Q: Write the equation of the hyperbola with eccentricity and foci at (0, 9) and (0, -1). 3</p><p>Q: Write the equation in standard form of the ellipse whose horizontal major radius has length 6 units, 2 whose center is at (2, -2) and = e . 3</p><p>Q: Write the equation in standard form of the hyperbola with center (1,2), a focus at 5 (1,2 + 5) and eccentricity . 2 Quadric Surfaces</p><p> x=2 to x=-2. Q1: What quadric surface will result from rotating y=3x about the x-axis from </p><p>Q2: Sketch a paraboloid given by y = x2 from x=2 to x=-2 rotated about the y-axis</p><p>Q3: The figure shows the paraboloid formed by rotating the graph of y = 9– x2, where x and y are in centimeters, about the y-axis. A cylinder is inscribed in the paraboloid, with its axis along the y-axis. The bottom base of the cylinder is at the origin, and the top base touches the inside of the paraboloid. The sample point (x, y) is on the parabola at the point where it touches the top base of the cylinder.</p><p>Write the volume of the cylinder as a function of x. Plot volume as a function of x. Sketch the graph. What is the maximum volume the cylinder can have?</p><p>Parametric Equations (x - 2)2 ( y+ 2)2 Q1. + = 1 36 20</p><p>Q2. Write the parametric equation of the circle that passes through (-1, 3) and has its center at (2, 4).</p><p>( y - 4)2 x2 Q3. - = 1 9 16</p>