Eliminate the parameter and obtoin the standerd formt 7,) of the rectongular equation. Circle: t=htrcos ce) ktrsin co) Use your result to equatons for the line or Conic set of parametric a ('When o <0L2TT) tircdle! center ? (9,2): radius :3

Q: Find the family of curve that intersects the family of hyperbolas y² = 2x² +b at an angle arctan(1).

A: To find the family of the curve that intersects the family of hyperbolas y2=2x2+b at an angle…

Q: Find an equation for the surface of revolution formed by revolving the curve in the indicated…

A: Given equation of curve is z = ln x The radius function about z axes is  r(z) = x = ez

Q: IS filled with circley The world around us Para bolas , e llipses and hyperbolas, In your post…

A:

Q: Let S be the quadric with equation 36x² – 4y² – 9z2 – 36x = 0 • Classify the graph of S…

A: Given, S is the quadric with the equation                                36x2-4y2-9z2-36x=0

Q: Find an equation of the largest sphere with center (3, 2, 6) and is contained in the first octant.…

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Q: snip

A: Given statement: A                  is the set of points P in the plane such that the ratio of the…

Q: Given the equation of an ellips in parametric form x = acost, y = bsint semi axes of the ellipse, t…

A: We have been given the parametric form of an ellipse x = acost, y == bsint where a, b are semi-axes…

Q: osen y

A: Is it sen y =x

Q: Find the standard equation of the sphere with the given characteristics. Center: (−4, 0, 0), tangent…

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Q: What is the relation of the conic section to the oblong plate?

A: Key Points A conic section (or simply conic) is a curve obtained as the intersection of the surface…

Q: In each part, find an equation of the sphere with center (5, –8, –2) and satisfying the given…

A: Given  Centre of sphere is =(5,-8,-2)

Q: A rod of given length (a+b) unit moves so that its ends are always on coordinates. Prove that the…

A: The two ends of the rod is always on coordinate axes. Let's take one end P of the rod is always on X…

Q: Identify the quadric surface with equation -a + 9y? – z = 0. O elliptic paraboloid O hyperbolic…

A: given  -x2+9y2-z=0

Q: In each part, find an equation of the sphere with center (2, –3, –3) and satisfying the given…

A:

Q: In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase.…

A: (a)From given information, x(t)=16cos5(2π)=16cos(10πt) y(t)=16sin5(2π)=16sin(10πt) z(t)=50t…

Q: Determine whether the statement"Every tangent line to a hyperbola intersects the hyperbola only at…

A: The tangent line at a particular point is unique as there are infinitely many points in the curve.

Q: Given a sphere in center-radius form, how will you get an equation tangent to only one of the…

A:

Q: In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase.…

A: Given information: The radius of the spiral is 29 feet and height is 60 feet that makes 6…

Q: Find the equation of the sphere in standard form that satisfies the given conditions. center C(-1,…

A: Equation of sphere  standard form of sphere equation

Q: The parametric curve x=2sin(t)+2, y=3cos(t)-2 describes a clockwise traveling  vertical ellipse with…

A:

Q: Find the differental equation of the family of plane curves described, Draw at least three members…

A: Formula: Circle equation (x-x1)2+(y-y1)2 =r2 given, Centre on y=x is (b,b) And radius =k

Q: Find parametric equations for the intersection of the surfaces y = x² and 2x² + y² + 6z² = 24 and…

A: Find out the parametric equations for the intersection of the surfaces y=x2 and 2x2+y2+6z2=24…

Q: Q2: A cube of edge 24mm is resting on the top of a frustum of cone of base diameter 60mm and top…

A: We are asked to draw the isometric view of the solid.

Q: Find an equation of the largest sphere with center (3, 2, 7) and is contained in the first octant.…

A:

Q: a) Find an equation of the sphere with center (1.-3,-5) and tangent to xz-plane.

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Q: Show by eliminating the parameter θ that the following parametric equations represent a hyperbola: x…

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase.…

A:

Q: In each part, find an equation of the sphere with center (−3, 5,−4) and satisfying the given…

A: Consider the given: a) Tangent to the xy−plane:x−−32+y−52+z−−42=−42x+32+y−52+z+42=16

Q: Write down the parametric equetions |3D 4=6-t in cartesion Form

A:

Q: Find an equation for the surface of revolution formed by revolving the curve in the indicated…

A:

Q: Let S be the quadric with equation 36x² –4y² –9z² – 36x = 0. Sketch a graph of the surface with…

A:

Q: 3. Find the area of the surface cut from the nose of the paraboloid x = 1-y²-z² by the yz-plane. Do…

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Q: Give a parametric description for a sphere with radius a, includingthe intervals for the parameters.

A: We will use the spherical coordinates for parametrization. Where ρ= radius= a And,

Q: A mirror for a reflecting telescope has the shape of a finite paraboloid of diameter 0.3 meters and…

A: Equation of a circular paraboloid  f=r24d here, f= focal length along the axis of symmetry from the…

Q: 9) Find a parameterization of the line formed by the intersection of the following planes: P,: 2x –…

A: Cross product of normals of planes is normal to the required line of intersection

Q: In each part, find an equation of the sphere with center (5, –8, –4) and satisfying the given…

A:

Q: Of the curve lying in the plane XZ-, (x - a) ^ 2 + z ^ 2 = r ^ 2 in R ^ 3 The region created by…

A: Given that the region is being created by rotating x-a2+z2=r2 in ℝ3 around the z-axis.  To find the…

Q: Find Parametric efuatins for the lines - The line through (1-2-2) Paralle tothe(Z)-axis.

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Q: Let Ci be the line segment from the origin to (3, 2,0); C2 be the shorter circular arc of the circle…

A: The three curves given are as follows: C1: The line segment from 0,0,0 to 3,2,0. C2: The circular…

Q: Eliminate the parameter in x = -t +2t and y =t-4 and then identify the parametric curve and sketch…

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Q: Find the diffetential equation of the family of plane curves described, Draw at least three members…

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Q: In 1932, Giuseppe Momo was commissioned to build the famous Vatican Museum double spiral staircase.…

A: Formula: The parametric equation for the helical path having radius r feet and height h feet that…

Q: Find the area of the surface obtained by rotating the curve of the following parametric equations…

A: We need to find surface area.

Q: Flnd the parametric equation of the line of ntersection of the planes and

A: First find normal vector then take cross product and use formula

Q: Find the equation of the tangent plane to the hyperboloid in 2 sheets x2 - y2 - z2 = 4 at the point…

A: We have to find the equation of the tangent plane to the hyperboloid x2-y2-z2=4 at the point 3,2,4.

Q: Identify the quadric surface as an ellipsoid, hyperboloid of one sheet, hyperboloid of two sheets,…

A: Here is the solution of the given problem.

Q: Give two parametric representations for the plane curve. 1. y#-4 y + 64 %3D

A: