and the plane - 3 X + Z Intersect along a line. Find Parametnic desenetion of this la

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 9x2 +…

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Q: Find parametrizations for the lines in which the planes x + y + z = 1, x + y = 2

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Q: The plane y=2 intersects the elliptic paraboloid ē =4x ty parabobo. Fied the slope ot the fangenh to…

A: Given :     y = 2      z = 4x2 + y2

Q: The distance between the centers-of the following two spheres: x²-22x+y2-58y+z?=-961,…

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Q: Find parametrizations The portion of the hemisphere x2 + y2 + z2 = 10, y>= 0, in the first octant

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Q: Which of the following is not a parametrization of the parabola y = r² ? Oz= Vt, y=t Oz-t, y-t Oz- ,…

A: We will check which parametrisation is correct.

Q: Find the distance between the skew lines with parametric equations x 2 + t, y = 1 + 6t, z = 2t, and…

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Q: Find parametrizations The portion of the plane 4x + 2y + 4z = 12 that lies above the square 0<=…

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Q: Let C be the curve of intersection of the parabolic cylinder x² = 2y, and the surface 3z = xy. Find…

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Q: Find a parametrization of the cylinder x2 + ( y - 3)2 = 9, 0 ≤z ≤ 5.

A: Given, the cylinder                         We have to find a parameterization of this given…

Q: Find a parametrization for the curve described below. the line segment with endpoints (- 2,4) and (-…

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Q: Use cos(t) and sin(t), with positive coefficients, to parametrize the intersection of the surfaces…

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Q: state whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an…

A: Rearrange the equation, 3x2-7y2=z by dividing both sides by 21 and obtain x27-y23=z21. The general…

Q: In which part of the (x, y) plane the following equation is elliptic? Uzr + 4ury + (x² + 4y*) uyy =…

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Q: Find a parametrization of the paraboloid given by f (x, y) = x 2 + y2.

A: To find a parameterization of the paraboloid given by: fx,y=x2+y2

Q: Find a parametrization of the line in which the planes x+y +z= -2 and y +z= 6 intersect.

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

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Q: Which of the following is not a parametrization of the parabola y = x² ? O x = /t, y=t O x = t, y=t…

A: To find out if the following given parametrizations are the parametrizations of parabola y=x2 x=t,…

Q: Find the point closest to the origin on the curve of intersection of the plane x + y + z = 1 and the…

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Q: Find the point lying on the intersection of the plane x + y +z = 0 and the sphere x2 + y2 + z? = 25…

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Q: Enclosed by the paraboloid z = x² + 3y? and the planes x = 0, y = 1, y = x, z = 0

A: We know that, volume under surface z=fx,y and above the region D in xy-plane is given as…

Q: Find parametrizations The portion of the paraboloid z =-(x2 + y2)/2 above the plane z =-2

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Q: PICTURE

A: We are given that the cone ax2+by2+z2 = 0 and the ellipsoid 2x2+4y2+z2 = 42 intersect and are…

Q: Find, correct to four decimal places, the length of the curve of intersection of the cylinder 25x2 +…

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Q: Find the distance between the skew lines with parametric equations  x = 1 + t, y = 3 + 6t, z = 2t,…

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Q: In the 3D coordinate system, for the quadric with euqation ax2 + y2 + 4z2+x + 6y − 4z = −a − 10…

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Q: Find the distance from a point P(x1, y1, Z1) to the plane Ax + By + Cz = D.

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Q: Evaluate (2y + 1) dS, where S is the part of the plane 2x+2y+z=6 that lies in the first octant.

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Q: Find /| F-dS if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = = 8-x?-y? lying…

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Q: Let C be the intersection curve of the parabolic cylinder √2x2 = 2y and the surface 3z =√2xy. Find…

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Q: 4 du + 3, du -o is dassified as Jhe P.O E dx² © Hyperbotic Elliptic Parabolic there of

A: 4∂2u∂x2+3∂2u∂x∂y=0

Q: Use sine and cosine to parametrize the intersection of the surfaces x² + y² = 16 and z = 4x³. r(t) =

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Q: Find the area of the ellipse cut from the plane z= 3x by the cylinder x + +y? =4

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Q: XydA, D is the triangular region with Vertices (0,0), Cu,0], and Cor) SketchD onthe XY planel

A: 8/3

Q: - I he symmetrie equidton of alne quation of alme Find the paramedic equation

A: Since you have asked multiple question, we will solve the first question for you. If you  want any…

Q: Which surface below is an elliptic paraboloid? O x^2 + y^2/4 - z^2 = 1 O z = -sqrt(x^2 + y^2) z =…

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Q: ce cut from the first octant by the cylinder z = 12 – 3y, and the plane x + y = 2

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Q: Find parametrizations The portion of the paraboloid y = 2(x2 + z2 ), y<=2, that lies above the…

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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: Let C be the curve of intersection of the parabolic cylinder x? = 2y, and the surface 3z = xy. Find…

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Q: The distance from a point S(xo, Yo, Zo) to a plane M: ax + by + cz + d = 0 is given by In PS| d :…

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Q: Identify the surfaces of equations in the Cartesian form. Show your complete solutions. (a) 2² = 4 +…

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Q: Find the real number a such that the line of x = 1, y = 2 – 1, z = 3 +t, parametric equations te R…

A: Given, parametric equations are                               x = t, y = 2-t, z = 3 +t, t in R To…

Q: Find the point lying on the intersection of the plane x + + z = 0 and the sphere x2 + y2 + z2 = 25…

A: According to the given information, it is required to find a point lying on the intersection of the…

Q: a) Evaluate //(-ri-yj+2: k) n dS, where a is the portion of the paraboloid : = 3r - 3y between the…

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Q: Find any points on the hyperboloid  x2 − y2 − z2 = 6  where the tangent plane is parallel to the…

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Q: 12. Find the distance from the point P(0,0,0) to the plane given by x + y +z= 6.

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Q: The position in feet, of a baseball t seconds after being thrown from third base to first base is…

A: A)                                t                        x=80 t             y=-16t2+24t+5 0…

Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.