Analytic geometry

It a parabola's focus is at (2, 5] and directrix is at y = 1, what is the vertex form of the equation representing this parabola? Oy=[m+2)z2 Oy=%(m+5)=+2 Oy=%{I3)E+3 What is the equation of the parbela shown below, given the focus at F{2, 5} and the directrix y = 1? Identify the vertex and the equation of the axis of symmetry of the parabola. O y 2 g 2):\" ~ 2; vertex {2,2}; axis of symmetry is a: = 5 O y = g: + 2)3 + 2; vertex {2, 2); axis of symmetry is s =- 2 O y = %(:I:+ 2): + 2 ; vertex (2,2); axis of symmetry is s =- 2 O y = (:r: + 2)2 + 2: vertex (2, 2); axis of symmetry is a = 2 What is the equation of the parbole shown below. given the focus at F(2. 5} and the directrix y = 1'? Identify the vertex and the equation of the axis of symmetry of the parabola. O y = : 2)? + 2; vertex {2,2}; axis of symmetry is m =5 O y 112(:C + it)2 + 2; vertex {2, 2]; axis of symmetry is a: = 2 O y : are + 2? + 2 ; vertex (23); axis of symmetry is a: = 2 O y = %(e + 2)2 + 2; vertex (2, 2); axis of symmetry is x = 2 The equation of a quadratic relation is y = as 3}2 l 3. Every point on this conic is equidistant from the focal point (a, ti) and the line defined by y : c. Determine the value of a. + b + c. 010 Find the centre and radius of the circle at\" + y\" 69: + 43 + 'i' = B. O centre (3, 2) radius w/E O centre (3,2), radius x/fi O centre [3, 2), radius \\ffi Q centre (3,2). radius 6 What is the equation of the circle with centre (in) and radius 6? _ 2 Q g +y2 = as 2 1 t 0 # +32 2 5 _ 2 O w + ya = 35 2 1 3 0 % +y3 = 6 Write the equation of a circle with centre (8, 3} which is tangent to the :eaxis. O {wB}E+(y-3)\"=9 O {w8}3+(y+3)\"=3 O {m8l2+(y+3)\"=9 O {3-3}2+(y-3l\"=3 Convert the following function given in Cartesian Coordinates into Polar form. :r: : 64 y2 64 0083 9 l 31113 6 64 cos2 6 linl\" 9 8 O r _ c056 , 51116 O r 2 i . . . . . . 50 . . A rubber ball is being spun In a outward spiral In a whirlpool defined by 7' - 62' where or g 6 S 47: as Shown in the diagram below. What is the vertical component of the ball's location, after it has spun through an angle of if? radians? O y : 0.98 O y= -1 '27 O y = -O.98 O y = 1 .17 What is the equation of the given ellipse? y A (-3, 2) (-1, -1.5) O (2+3)2 2(y + 1.5)2 2 .= 1 O (2+3)2 4(3 + 1.5)3 49 = 1 O (2 + 3)2 49(y + 1.5)3 O (2 + 3)2 + 4(y + 1.5)2 49 The point (2v/3, k) lies on the ellipse 2, + 1 = 1. Which of the following could be a value for k? O 3 v/5 2 O 4V/3 0 3 0 4 An ellipse has centre (0, 0) and vertices on the y-axis. The minor axis has length 10 and the major axis has length 14. Find the equation of the ellipse. 100 + 796 K= 1 25 4 49 - 1 25 =1What are the slopes of the asymptotes of the hyperbola 4 = -1? O+2 What is the equation of the line that contains the vertices of the hyperbola (a + 4)3 (3+ 2)3 = -1? 9 16 Oy =-2 O y = 2 Oz =4 Or=-4 Convert the following parametric curve into Cartesian form: * = 4sint, y = 5 sint None of these. O x2 + y? = 20 5x2 + 4y? = 1 O - + 5 Which of the following is a parameterization of the line that passes through the point (1, -3) with a slope of -2? Ox = t +3 andy = 4t + 1, for any t O x = -2t and y = 2t - 1, for any t O = = 2t and y = -4t - 2, for any t O x = tant and y = -2tan -1, for - 7 A particle moves in the xy plane so that at any time 0