Identify and sketch the surfaces: Note: Alway bring equations to the standard form first, then use your knowledge of 2-D to sketch in appropriate 3-D, a) x² + y² − 2z² + 10x – 4y – 2z = 0 b) x² - 4y + z² = 4 c) z² = 3y

Q: 1. Put the following equations in standard form and find the center point and the radius: a) x-2x+y…

A: Given that

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Q: iv) y=-x- 3 1 v) y=-2x+ vi) y=;* 1 21 y y y 1 =-2.5 1 2 2 y y y 2 2 2 -2 -2 -2 2 -2 2 2 y-intercept:…

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Q: 3. x²-6x-y+3=0 Standard Form Equation: a. Vertex: b. Focus: c. Length of LR: d. Directrix: PCLNIIS…

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Q: Which of the following correctly depicts the sphere given by the equation: x2 + (y - 2)2 + (z - 2)2…

A: Given: x2 + (y - 2)2 + (z - 2)2 = 4

Q: Q: Discuss find following surfaces Traces. the intercepts and 4x₁²² + 44.² + Z² - 16 = 0

A: Given: Equation of surface 4x2+4y2+z2-16=0 To find: The value of intercept and traces.

Q: Provide a hand-drawn sketch of S using the traces obtained in (a). Label all important points found…

A: As per the question we are given a 3d surface S defined as : 4x2 - (y-3)2 + 4z2 = 4 And we have to…

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Q: 5) Classify the surfaces, listing shape, location, and orientation: a. 4(x-1)2 + 9y+1)² + z² = 36…

A: Given:  4(x-1)2+9(y+1)2+z2=36 ⇒4(x-1)236+9(y+1)236+z236=1⇒(x-1)29+(y+1)24+z236=1 This is of the form…

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Q: Evaluate (x+ y)ds, where C is the top half of the circle x² + y² = 4, oriented counterclockwise.

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Q: Explain why the equation 7 = (-1,0, -1) + s(2,3,-4) + t(4,6,-8) where s, t ER does not represent the…

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