2) The Cartesian coordinates are given for a point: (x, y) = (-3, –3/3). Find polar coordinates (r, 0) of the point where (i) r > 0, 0 > 0 (ii) r < 0, 0 > 0

Q: Find the length of the polar spiral r = 0² from 0 < 0 < V5.

A:

Q: 7. (a) Find a spherical coordinate equations; for the sphere x²+y²+(z-1)²=1 and the surface…

A: To convert a point from Cartesian coordinates to spherical coordinates, use equations…

Q: Describe how the surface with spherical equation p²(1 + A cos² ¢) = 1 depends on the constant A.

A: Given : ρ2(1+Acos2ϕ)=1To describe: How the surface with spherical equation  ρ2(1+Acos2ϕ)=1depends on…

Q: Match the surface to its corresponding equation in spherical coordinates. |p = 4 cos() 1.5 -1 -0.5 0…

A: To match the given surface to their given Equation in spherical coordinates.

Q: Match the surface to its corresponding equation in spherical coordinates. 37 4 -3 -2 -1 0 1 2 3 3…

A: To solve this we have to find the relation of equation

Q: Find the length of the polar curve: r = cos 0, where 0 < 0 < 2n.

A: We need to find the length of the polar curve

Q: (x, y) of the point with polar coordinates What are the Cartesian coordinates (r, 0) = (4, 5 ) ? O…

A: Given (x, y) = 4, π6

Q: Use the parametric equations of an ellipse, æ = 2 cos(0), y = 5 sin(0), 0 < 0 < 27, to find the area…

A: Given :  x=2cos(θ), y=5sin(θ),  0≤θ≤2π The area under the curve can be written as:…

Q: 3. Evaluate/calculate using polar coordinates. -1/2 cV1-x² А. M-X" xy/x2 + y² dydx ху,

A:

Q: Convert to polar coordinates in the xz-plane, similar to Example 3 in the book. r2 63 – 2x? – 2z? –…

A: The limits lead to interpretation that,   From (2), Comparing the above result with  r=3

Q: Find the Cartesian equation for the curve represented by the polar equation, r = 2 sin 0. O x² + y²…

A:

Q: Find the length of the curve r = 2 sin^3 (u/3), 0 … u … 3pi , in the polar coordinate plane.

A: Given:        r=2sin3u3,  0≤u≤3π

Q: Find a polar equation for the curve represented by the given Cartesian equation. (Assume 0 ≤ 0 <…

A:

Q: Find a set of parametric equations for the curve of intersection of the cylinder (x - 1)2 + y2/4 = 1…

A: Given: The equation of cylinder is: x-12+y24=1 .....(1) The equation of paraboloid is: x2+y-22=z…

Q: For spherical polar coordinate system (3² exp(x)sin Cosø 4/2 `a 1 -Zr,„Zr. 2a a |W„Y„dV = 8¸ = ? px…

A:

Q: Identify the surface whose equation in spherical coordinates is given by p= 2 cos o

A:

Q: Find two other pairs of polar coordinates of the given polar coordinate, one with r>0 and one with r…

A:

Q: 3. Express the equation y = mx + b, where m and b are constants, in plane polar coordinate.

A: Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: Find an equation in rectangular coordinates for the surface represented by the cylindrical equation…

A: Cylindrical co-ordinates of the point P are (r,θ,z) rectangular co-ordinates of the point P are…

Q: Given the curve in polar equation r = 8 cos 0, 0<0 Use integration to find the area of surface…

A: Given the curve in polar equationr=8 cos θ, 0≤θ≤π2.By using the integration to find the area of…

Q: 4. Find the equation of the plane that passes through the point (5, –1,0), and is per- pendicular to…

A: Let's find.

Q: For spherical polar coordinate system 1 Z -Zr Zr 3/2 4/2 a exp(-()sin OCoso 2a px a V WmdV = 8 = ?…

A:

Q: 9. Show that for a ± 0, the equation p = 2a sino cos 0 in spherical coordinates describes a sphere…

A: Given :  The equation ρ = 2 a sin ϕ  cosθ  .   To determine: The equation ρ = 2 a sin ϕ  cosθ  in…

Q: 1. Eliminate the parameter to find a Cartesian equation of the curve with parametric equations z =…

A:

Q: Find a polar equation for the curve represented by the given Cartesian equation. (Assume 0 ≤ 0 <…

A:

Q: Identify the surface whose equation in spherical coordinates is given by p= 8 cos o

A:

Q: Given the curve of intersection of the x² + 4y² -z = 0 which is a paraboloid and the plane 2x - z =…

A: Solution:-

Q: 7T What are the rectangular coordinates of the point with polar coordinates (r, 0) = [2, ? 4 (х, у)…

A: Given: r,θ=2,7π4

Q: Does the origin lie on the polar curve r = 1 – 3cose ? Explain.

A: We will first plot the polar curve in the 2D (r,θ) plane with polar coordinates. We shall plot it…

Q: 9. (a) Find the equation of the cone 3.x2 +3y2 in spherical polar coordinates. (b) Use spherical…

A: Given

Q: Show that every vertical line in the xy-plane has a polar equation of the form r = a sec θ

A:

Q: Find an equation in spherical coordinates for the surface represented by the rectangular equation.…

A:

Q: Identify the surface whose equation in spherical coordinates is given by p = 2 cos o %D

A:

Q: 9. The Whitney umbrella surface is given parametrically by I= uv, y = v, 2= u. A picture of this…

A:

Q: Find the distance on the xy plane between the two points, given below as polar coordinates (7,…

A:

Q: Show that the parametric equations x a cosh u cos v, y b cosh u sin v c sinh u represent a…

A:

Q: Gz find the Velume of the Selid with in the cylinder xya16 and between the y-2-3 and Z=2(polar)…

A:

Q: Use the parametric equations of an ellipse, x = 2 cos(8), y = 3 sin(8), 0 < 0 < 27, to find the area…

A:

Q: Identify the surface whose equation in spherical coordinates is given by p = 8 cos %3D

A: The given equation in the spherical polar co-ordinates is ρ=8cosϕ. In spherical polar co-ordinates,…

Q: Find the points of horizontal tangency to the polar curve. r 2 csc 0+3 050<2x (smaller r-value) (r.…

A:

Q: Consider a sphere E with center at the origin and radius equal to 1, following the Beltrami-Klein…

A: Determine the parametric equation by first determining the equation of the line and then…

Q: . Show that the equations x = r cos 0, y = r sin 0 transform the polar equation 1 + e cos 0 into the…

A:

Q: Find the length of the curve r= /1+ cos 20, 0<0<n/2/6. The length of the polar curve is.

A: We know the arc length formula for polar coordinates is L=∫θ1θ2r2+drdθ2dθ. Here, r=1+cos(2θ),…

Q: i need to convert below z=64-4*x^2-4*y^2 and above the xy-plane into polar coordinate however i am…

A:

Q: 11.) Find a rectangular equation for the Surface whose Spherical equation is a sin ($) Sin (e)

A:

Q: Find the polar equation for the Cartesian curve ² Or 1 T= cos 2 1 Or=sin @tan 0 2 T = Or= Or T = 1 1…

A: The given cartesian curve x2=y2 we have to find the polar equation

Q: 6. Find the projection of u = -7 onto the -2 line e of R given by the parametric equation l = tũ, -1…

A:

Q: Show that the polar equation for the curve with Cartesian equation x² – y² = 1 is r? = sec 20.4

A: