Consider the surface S₂ with equation(x - 1)² y² 229 3+4a) Find an equation of the trace of S₂ on the xy-plane, the xz-plane, the plane x = 1, and theplanes z = 13. Identify the type of conic each trace represents.b) What type of quadric surface is S₂?c) Sketch the graph of S₂ using the traces obtained in 3.a). Label all important points found oneach trace.-= 1.

The given surface is S2 : x-124+y29-z23=1. (a) To Find and To Explain the type of conics that each…

Answered: 1)² y² Consider the surface S₂ with…

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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44. The parametric equation of the rectangular hyperbola #(y + 1) = c² is A. 1 = ct, y B. I = 1+ ct, C. z = ct, y = - I = D. I = ct, y =
Find parametric equations for the path of a particle that moves along the circle x² + (y - 2)2 = 36 in the manner described. (Enter your answers as comma-separated lists of equations. Use t as the parameter.) (a) Once around clockwise, starting at (6, 2). ,0sts 2T (b) Three times around counterclockwise, starting at (6, 2). ,0sts 6n (c) Halfway around counterclockwise, starting at (0, 8). 3n
23. What is the center of the ellipse with the equation (x-7)2 (y+4)2 1 ? 16 25 a. (7,4) b. (-7,4) c. (-4,7) d. (4, -7) e. (4,5) 24. Given: cos A = ² , A is in QIV, sin B = -12 180°
Consider the conic section given by the polar equation 4 1-sin 0 (a) (b) (c) (d) r = Without converting into Cartesian form, identify the conic section represented by the equation above. Write out, with justification, the directrix and the focus (or foci) of the conic section. Determine the exact length of the curve of the conic section from 0 = 0 to 0 = π/6. Explain whether the tangent of the curve at the point where 0 = π/4 is orthog- onal to the line y = √2x+1.
2. The temperature at the point (r, y, z) of space is determined by: k T(, y, z) a3 + y3 + z2 where k is a constant value. (a) We know that temperature at point (0, 0, 1) is 250. Find the value of k. (b) Find the rate of change of temperature at point (2, 1, 2) in the direction of (3, 1, 2). (c) In which direction from (2, 1, 2) does the temperature decrease most rapidly. DI have completed answering this question on paper.
Consider the conic section given by the polar equation 4 1-sin 0 (a) (b) (c) (d) r = Without converting into Cartesian form, identify the conic section represented by the equation above. Write out, with justification, the directrix and the focus (or foci) of the conic section. Determine the exact length of the curve of the conic section from 0 = 0 to 0 = π/6. Explain whether the tangent of the curve at the point where 0 = π/4 is orthog- onal to the line y = √√2x+1.
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