Write the equations in cylindrical coordinates. (a) 8x2 - 6x + 8y2 + z? = 9 (b) z = 8x2 – 8y2

Q: Complete the square: x² + 3x+ r_52+ =_x² + ²x+ = (x+ = (x+ )². )². )².

A: The given expressions

Q: Find the equation of a sphere if one of its diameters has endpoints: (-10, -12, -13) and (4, 2, 1).…

A:

Q: Convert r=sqrt(3) into a rectangular equation

A: Answer

Q: Write the equation of the parabola given by y? + 2y + 12x – 23 = 0 in standard form. %3D -

A: Given equation of parabola is y2 + 2y + 12x - 23 = 0

Q: 1. Which of the following is a complex solution to the equation: (x+3)* -4 =-40? (1) 3+7i (3) -3 +6i…

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Q: Identify the quadratic surface of the equation 6x? + 3y? + 222 + 24x – 6y – 12z + 39 = 0 Choose an…

A: Given, 6x ^ 2 + 3y ^ 2 + 2z ^ 2 + 24x - 6y - 12z + 39 = 0

Q: 4. Find all solutions in the complex numbers to the following equations. (a) z5 = z. (b) 24 = iz².

A:

Q: 4. Convert the equation (x = 10 + 5t : 10 - 2t = to scalar form.

A: Given the problem that the parametric equation is x=10+5ty=10−2tthe aim is to write the equation in…

Q: Use geometry to show that (x2-y2)= (x+y) (x-y). Use a square in a square.

A: Consider the diagram:

Q: Solve: Vx + 2 - 2 = 0.

A:

Q: Find the quadratic equation whose graph has vertex (3, 1) and passes through the point (2, 0) using…

A: Given:- Find the quadratic equation whose graph has vertex (3, 1) and passes through the point (2,…

Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

Q: 3x2 − 2y2 + 18x + 8y + 13 = 0 directrix:

A: Given equation is 3x2-2y2+18x+8y+13=0. Given equation can  be written as:…

Q: Find the value of y in the complex equation (2x-3yi(3 + 4i) 78-21i O5 -3 03 -4

A: Given, (2x-3yi)(3+4i)=78-21i Expanding the LHS⇒ (2x-3yi)(3+4i)=6x+8xi-9yi-12yi2…

Q: Complete the square: x²+x+49/36 x²-x+ 14/5 x²+x+ 1/9 = (x+ 7/6 = (x+ = (x+ = -5/14 1/3 )². )². )².

A: We need to complete the square.