1.5a =Xb0.50-0.5-1.5C =-6-4-20y24T4310-1-2222For the above plot of the one sheeted hyperboloid^ ( ² ) ² + ( ² ) ² − ( ² ) ²-a= 1, find theparameters a, b and c. Note that a, b and c are positive integers between 1 and 6 inclusive. Usethe mouse to rotate the surface.-34

To find the values of the parameters of the hyperboloid.

Answered: 1.5 1 a = 0.5 0 b = -0.5 -1.5 9 C= 4 -2…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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11. Let E be the region in the plane between the two ellipses 4x² +9y² = 1 and 4x² +9y² = 4. Evaluate ff x²y dA.
Ddf
4. Consider the following parabola with the focus at (6,2) and the directrix line at y = -6. y 107 9 8 7 * (x, y) (6,2) -10-9-8-7 -3 -2 -1 0 7 -1 -2 -3 -4 -5 -7 -8 -10, 10% y = -6 9 10 x Part A: Use the distance formula to describe the distance from (x, y) to the focus. Part B: Use the distance formula to describe the distance from (x, y) to the directrix. Part C: Write the equation for the quadratic in standard form. Part D: Write the equation for the quadratic in vertex form. 5. A parabola has a focus of (4,-5) and the directrix is y = 8. Which of the following functions model the parabola with the characteristics above? Select all that apply. 0 x²-x+ □y=(x² - 8x - 23) 16 □(x-4)² +5 ☐ □ - x² + 3x + ² -(x-4)² +22 □ -(x-4)² + 6. A parabola has a focus located at (.) and a directrix at y =² What is the equation for the parabola in standard form? B A y = ²x²_ -x+ 15 16 y=-x² + 2x y=- ²x² + -²x² + Dy=-= 8 15 16 77 128 - -x 5 16 69 100 77 128
3. 43. What is the length of the transverse axis of the graph of +2)* (x-1)* 12 16 A. 1 unit B. 2 units C. 4 units D. 6 units 44. Write an equation of a hyperbola with center (-4, 6) and vertices at (-8, 6) and (O, 6). Graph the hyperbola. (x+4)2 y-6)2 A. 3D1 19 R (y-16)2 (x+4)2 3D1 C. U+6)? (x-4)2 D. 16 (x-4)2 +6)2 %3D1 3D1 16 16 6. 16 9. に 45. Write anequation of a circle with center (-5, 8) and radius 2. A. (x + 5)2 + -8)2 = 2 B. (x- 5)2 + (y + 8)2 = 2 46. Which of the following is a solution to this system of nonlinear equations? (-y2-36x + 2y- 37 0 3x +y = 1 C. (x-5)2 + (y + 8)2 = 4 D. (x + 5)2 + (y-8)2 = 4 %3D A. (2,7) B. (0,3) C. (7,2) D. (4,-4) 2.
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25. What is the standard equation of the hyperbola whose foci are F1(-4v2, 0) and F2(4V2, 0), such that for any point on it, with an absolute difference of 6? A. 9. x2 y = 1 В. 25 x2 y = 1 D. 25 y = 1 16 16 9. 16 16
What are the xy, yz, and xz traces if they exist and the type of surface (hyperboloid, etc) for the following:1. x2/25 + 9y2-4z2 -9 = 0 2. z = x2/25 - 9y2
Which of the following is an equation of a Hyperboloid of Two Sheets? O z² = 1 - x² - y² Ox2 - y2 - z² = 0 Ox2 - y2 - z² = - 1 x2 + y2 + 1 = z² O z = - x2 - y2²
Q2. Consider a unit square with vertices A (0, 2) B (1, 1) C (1, 2) and D (0, 0). Find the resultant vertices A', B', C' and D' of the transformed square after the following transformations. Sh = 1.5, yref =-3 Shy =3, Xref= -4 iii. i. ii. Reflection on X-axis
A. Ellipse B. Parabola C. Hyperbola
5. The equation of the circle whose center is the centroid of the triangle with venices (-72 (4,-3) and (6, -5) and passes through (4,2) is ....
12. If (f, 0) is the focus of the parabola given by y? = 12x, and (h, k) is the center of the hyperbola given by x-y - 6x – 8y = 8, find f+ h+ k. A. -2 В. -1 С.О D. 1 E. 2

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1.5 1 a = 0.5 0 b = -0.5 -1.5 9 C= 4 -2 0 2 For the above plot of the one sheeted hyperboloid (2)² + (%)² – ( - ) ² 2 4 6 4 3 2 1 0 -1 -2 డి 4 parameters a, b and c. Note that a, b and c are positive integers between 1 and 6 inclusive. Use the mouse to rotate the surface. Z = 1, find the