The equation of a surface in cylindrical coordinates (r, 0, z) is z = r²cos(20). The equation of the surface expressed in Cartesian coordinates (x, y, z) is given by : Oz=x²-y² Oz = 2x√√x² + y2 Oz = 2x√√x² - y2 Oz= x² + y² Oz = 2y√x² + y2 Oz=y²-x² z = 2y√√y2-x2

Q: The paraboloid  z = 8 − x − x2 − 4y2  intersects the plane x = 3 in a parabola. Find parametric…

A: The given paraboloid is z=8-x-x2-4y2 which intersects the plane x=3 at the point 3,2,-20

Q: Find the distance from the point (−1, −2, −3) to the plane 4x - 4y + 4z = 3.

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Q: Find the center-radius form of the equation of a sphere which circumscribes two externally tangent…

A: It is given that the equations of the sphere are x2+y2+z2-2x+2y-4z-19=0 and…

Q: Find the distance between the point (-1,–1,2) and the plane 2.x+5y-6z =4

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Q: find the points on the surface

A: Given, S: x2-y2+6z=0=fx,y,z where normal line to the surface is parallel to the line passing through…

Q: Suppose C is the line y = 5-2x in the xy-plane. Determine parametric and Cartesian equations of the…

A: Given the line equation C in xy-plane is y=5-2x     put x = k,  in above line . k be a parameter…

Q: A laser pointer is situated at the point (3, 1, 4) and is pointing a linear beam in the direction…

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Q: Find the parametric equation for the line where the planes 7x – 6y + z = 10 and 2x + y – 3z = 4…

A: We have, r(t) = (0, -2, -2) + t(17, 23, 19) The detailed solution is as follows below:

Q: A surface is defined by the following equation: 9x2 + 16y2 + 9z2 = 25. Sketch the intersection…

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Q: Write x²-y²-(z-1)²=9 in cylindrical system and what surface does it represent

A: A given point P (x, y, z) in rectangular coordinate. Now in a cylinder coordinate system, a point is…