4. Identify and sketch the conic sections and quadratic surfaces of equation Q() when Q(r) is...
4. Identify and sketch the conic sections and quadratic surfaces of equation Q(x) - 1, when Q(x) is a quadratic form defined by one of the following matrices (b) 1 2 1 (c)0 0 0 3 0 -1 2 4 -3 (d)4 1 3
4. Identify and sketch the conic sections and quadratic surfaces of equation Q(x) - 1, when Q(x) is a quadratic form defined by one of the following matrices (b) 1 2 1 (c)0 0 0 3...
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7) Conic sections stuff! a Sketch the following conic section AND find an equation of the conic section that satisfies the given information Ellipse, center(1,3), vertex(1,0), focus(1,5) b. Find the eccentricity, identify the type of conic, find the orientation (vertical or horizontal), and give the equation of the directrix. 3 2 + 5 sin(0)
Investigation 4: Quadratic Equations The quadratic equation is typically written in the form and has the solution 2a In this Investigation, we will look at a number of equations, rearrange them to be in this form, and identify which variables correspond to a, b, c, & x in the definition above. Activity 1-8: For each of the expressions, do the following Is it absolutely necessa ry to use the quadratic equation to solve the expression? . egardless of whether you...
1.) Put the conic in standord form by completing the square,
please identify which conic it is, and then graph the conic
section. Also label each relevant point or asymptotes. Sketch your
x - y axis and the conic, and labl the scale on the axes.
example sketches:
2.)
c. -9x2 + y2 – 72x – 153 = 0 Ex. 1 Sketch (x-5) V =2 center: (5,2) radius: 2 Center , horizontal: 2 units left/right 3 units up/down (1,3) 13,0)...
CONIC SECTIONS Graphing a hyperbola given its equation in standard form v + Х Graph the hyperbola. please box where to put points (y+4) (x-5) 1 25 16 14 0 3 UN P 12
10.(5 points) a). Find the eccentricity; b) identify the conic; c) give an equation of the directrix; d). sketch the conic. 7+5 sine
6. Consider the function Q(z) = Az[+ B2:1x2+ Cr where A, B, and C are numbers not all zero, = 0 and the level sets of the associated quadratic form; and recall the well-known classification rule for conic sections by the discriminant (B2 -4AC): if B2 - 4AC < 0, then the conic is an ellipse; if B2-4AC = 0, then the conic is an parabola; and if B2-4AC > 0, then the conic is a hyperbola. (a) Complete the...
General Equation of a Conic:
(a) Determine the Type of Conic
I figured out that its a hyperbola: ac - b2 =
(-1/4)
(b) Determine if the Conic is Degenerate
I figured out that its not degenerate: acf + 2bde -
ae2 - b2f - cd2 = 1
(c) Sketch a graph of the Conic without using a graphing
calculator
I am stuck on part (c) I assume you would try to get it to the
general form of the...
3) Consider the equation of the conic below. (4 pts) a. Determine which conic This equation represents. State the conic and explain your decision 3x² + 2y? - 15x + 20y - 4 = 0 Rewrite this equation with a minor change so that the equation now represents the following conic b. circle c. hyperbola d. parabola 1) Use the animation mentioned earlier on page 910 to create two graphs of two ellipses using the instructions below. (3 pts each)....
16x2-y2 + 42. 16-0. Identify and sketch the surface EXAMPLE 7 Dividing by -16, we first put the equation into standard form: SOLUTION z2 16 4 Comparing this equation with equations of quadratic surfaces, we see that it represents a hyperboloid of two sheets the only difference being that in this case the axis of the hyperboloid is the y-axis The traces in the xy and yz-planes are the hyperbolas 16 and z2 =1 4 x=0. 16 The surface has...