5. (a) Find a parameterization of the intersection of the cylinder 4x² +9y² = 36 and the plane z = 3x - 4y. (b) Via a graph of the cylinder and plane, sketch the curve of intersection. Based on your parametrization in (a), indicate the orientation of your parametrization.

Q: Define parametrization.

A: Parameterization is the process of finding parametric equations…

Q: The surface of a paraboloid results from rotating a parabola about it's axis. The parametric form is…

A: 1 )Equation of a Parabola:The standard equation of a parabola in the xy-plane is given by  where a…

Q: (b) Find a line in the plane x + y + z = 3 that is perpendicular to the line with parametric form…

A: The intersection between the given line and plane the intersection point

Q: 2. Convert the point (V6, , v2 ) from cylindrical to spherical coordinates. (12등, ) (b) (vZ;. )…

A:

Q: Give a scalar equation for a plane at distance 9 from the plane P with equation -2x+2y-z = 3. 0=0

A:

Q: Find and equatin for the parabolid z = x^2+y^2 in spherical coordinates

A: Given query is to find equation of paraboloid in spheo coordinates.

Q: A glass sphere given by the equation (-1)+(y-2)²+(-3)² = 36 is floating above the plane 2x+y-2x =…

A:

Q: Explain whether the cylindrical surface and the spherical surface may be homeomorphic?

A: To explain: Whether there is a chance that the spherical and cylindrical surfaces are homomorphic.

Q: Determine the surface area of the solid obtained by rotating the following parametric curve about…

A: Given: x=9+t2, y=2t, 0≤t≤2

Q: 36 for 0 <= u <= 6 and 0 <= v <= 2(pi) where <= is less then equal too where pi = 3.1415

A: Introduction: An ellipse is the locus of all points that satisfy the equations.x = a sint,  y = b…

Q: Where does the parametric line ( 2 + 2 t , t , t ) intersect the plane x+y-3z=4?

A:

Q: Find the lines curvatures, the first and second fundamental forms of the surface: the surface

A: As per the question we are given a surface. And we have to find its first and second fundamental…

Q: Find an equation of the tangent plane to the parametric surface

A:

Q: Find the cylindrical equation for the surface whose rectangular equation is x² + y² - 2y = 0.

A: Given rectangular equation is,We have to find cylindrical equation for the surface.

Q: /Sketch the Surface Z=V9-X+y- and verify that fxg = Exx %31

A: Second order Partial Differentiation

Q: Find the equation oftangent plane and normal lines ofthe surface: f(x,y, z) = 10x² –14 y² +11z³-7 at…

A:

Q: a) A curve can be parametrized by calculating its intersection point with the line y = tx, in which…

A:

Q: 2. Convert the point (V6, , V2 ) from cylindrical to spherical coordinates. (a) (V2,플, ) (b) (vz. )…

A: Option C is correct answer.

Q: / (2² + y²) do, where S is the portion of the sphere r? + y? + z² = 9 in the first octant that is…

A:

Q: tangent plane at the point (-2,1 – 3)

A: Equation of the tangent plane = dfdxx-x0+dfdyy-y0+dfdzz-z0 Let f=x24+y2+z29-3 (given)

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A:

Q: 2. Convert the point (V6, , v2) from cylindrical to spherical coordinates. (e) (2VZ,품, 끌) (d) (vZ )…

A: The solution is given as

Q: x = −5+2s 32. a) Convert the plane to scalar form. ₁: y = -3s + 2t z = −1+t 32. b) Determine how the…

A:

Q: Consider the paraboloid given by the equation: z = x^2 + y^2 Find the equation of the tangent…

A: at point (1, 2, 5)at point (1, 2, 5)

Q: y² - (z²/3) = 1 + (x²/12) sketch the quadric surface. emphasize the traces on the coordinate planes…

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A: