Find the equation of the tangent plane to the hyperboloid in 2 sheets x2 - y2 - z2 = 4 at the point (3,2,4).

Q: Find the equation of the tangent plane to the surface y = 2x2 - z at the point %3D (0, -1,-2) y+2z =…

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Q: Obtain all the umbilical point of the Hyperboloid of two sheets {x^2+y^2-z^2=1}.

A: consider the equation {x2+y2-z2=1}

Q: Find the radius of curvature of a parabola y² - 4x = 0 at the point (4,4). 2

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Q: 1. Find all points Po on the ellipsoid 2x2 + 3y? + 2z2 plane x – 3y + 2z = 5. = 22 at which the…

A: To find points P0 on the ellipsoid 2x2+3y2+2z2=22   The tangent plane is parallel to the plane…

Q: Find the radius of curvature of the parabola y² = 4px at (0, 0).

A: Given that the parabola y² = 4px  To Find the radius of curvature of the given parabola at (0,0).…

Q: Use the parametric equations of an ellipse, x = 5 cos (0), y = 4 sin(0), 0≤ 0 ≤ 2π, to find the area…

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Q: Find a point on the hyperboloid x2 + 4y2 – z2 = 1 where the tangent plane is parallel to the plane x…

A: Given  and plane

Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid z =x²…

A: Tangent line to ellipse will be perpendicular to normals of both the surfaces Therefore,  The…

Q: Find parametric equations of the tangent line to the curve of intersection of paraboloid z = x² + y²…

A: We know that tangent line to ellipse will be perpendicular to normal of both the surface. Therefore,…

Q: Find the standard equation of the sphere with center (−3, 2, 4) that is tangent to the plane given…

A: Radius (r) will be the distance from the center to the tangent plane. That is the distance between…

Q: Find the standard equation of the sphere with center (-4, 3, 8) that is tangent to the plane given…

A: The center of the sphere is (-4,3,8) . The tangent plane is 3x+8y-4z=24 The radius of the sphere is…

Q: Find the equation for the tangent plane to the surface Z =-8x² - 3y2 at the point (2 1, -35). O 2x +…

A: We can find the answer as below

Q: Compute the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder…

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Q: Show that the cylindrical equationr 2(1 − 2 sin2 θ ) + z 2= 1is a hyperboloid of one sheet.

A: The cylindrical co-ordinates is converted into rectangular co-ordinate as x=rcosθ         ⋯⋯1y=rsinθ…

Q: Find parametric equations of the tangent line to the curve of intersectic paraboloid z = x² +y? and…

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Q: Find an equation of the sphere with center (2, 1,−3) that is tangent to the plane x −3y + 2z = 4.

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Q: Identify a generating curve on the rz-plane for the surface of revolution with equation 1² + y³ + z²…

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Q: Find a Cartesian equation for theplane tangent to the hyperboloid x2 + y2 - z2 = 25 at the point(x0,…

A: If a hyperboloid is defined as f(x,y,z)=0, then the tangent plane at the point (a, b, c) is:…

Q: Determine the parametric equations of the curve of of the ellipsoid 4x² + y2 + 4z2 = 4 and the…

A: Solution: Given equation:ellipsoid: 4x2+y2+4z2=4; and half−cone: y2=x2+2z2 To find: parametric…

Q: Find the orthogonal trajectories for the family of ellipses with centers at the origin and…

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Q: Find parametric equations for the tangent line to the curve of intersection of the paraboloid   z =…

A: The given curve is the intersection of paraboloid z = x2+y2 and ellipsoid 3x2+2y2+6z2 = 29.

Q: Find all points on the ellipsoid 2x² + 3y² + 4z² = 9at which the plane tangent to the ellipsoid is…

A: Explanation: Given that,  Ellipsoid:2x2+3y2+4z2=9Plane:x-2y+3z=5⇒15x-25y+35z=1   Suppose point of…

Q: The surface z - - = 1 is a hyperboloid of one sheet. Select one: True False

A: The general form of the equation of hyperboloid of one sheet is: x2a2+y2b2-z2c2=1

Q: A reflecting telescope contains a mirror shaped like a paraboloid of revolution.If the mirror is 4…

A: When we draw the parabola  to form the mirror on a rectangular coordinate system  we find…

Q: Show that the cylindrical equation ,2(1 – 2 sin² 0) + z² = 1 is a hyperboloid of one sheet.

A: Given a cylindrical equation r21-2sin2θ+z2=1 To show that this equation is a hyperboloid of one…

Q: Find a parametrization for the sphere of radius 2.

A: Consider the equation of the sphere x2+y2+z2=22. Here the sphere is centered at origin.

Q: Find the points on the hyperbolic cylinder x2 - z2 -1 = 0 that are closest to the origin. please…

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Q: Find equation of the tangent plane to the given surface at the specified point. 5x^2+3y^2+8z^2,…

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Q: Are there any points on the hyperboloid x 2 − y 2 − z 2 = 1 where the tangent plane is parallel to…

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Q: Find the centroid of a thin, flat plate covering the region enclosed by the parabolas y = 2x2 and y…

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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: Find the equation of the tangent line to right branch of the hyperbola x = sec t, y tant, -sts at…

A: Given query is to find the equation of tangent line.

Q: . Find the area of the surface generated when the curve y = x* 1 + ,on [1,2] is rotated about the…

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Q: Find the y coordinate of the center of curvature of th parabola at (2,2).

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

A: Surface area in yz-plane

Q: Find the equation of the tangent plane to the sphere x² + y2 + z² = 1 at the point (1/ V3, 1/V3, 1/…

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Q: Find the points on the hyperbolic cylinder x2 - z2 -1 =0 that are closest to the origin. please…

A: The parametric equation of hyperbolic cylinderx2-z2-1=0 is , x=cos hθ                          y=y…

Q: Find the standard equation of the sphere with center (-6, 2, 7) that is tangent to the plane given…

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Q: determine a and b as to make the cylinder y^2=4ax orthogonal to the ellipsoid at point (1,2,1)

A: Given equation of the cylinder is  y2=4ax, say φ1=y2-4ax=0 and the general equation of the ellipsoid…

Q: Identify a generating curve on the rz-plane for the surface of revolution with equation 1² + y² + zª…

A: The equation of the surface of revolution given is as follows:…

Q: Find an equation for the tangent plane to the hyperboloid x2+y2−z2=1 at the point (3,1,3).

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Q: Find the y coordinate of the center of curvature of the parabola at (2,2). 7. -7 -6 6.

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Q: Are there any points on the hyperboloid x² – y² – 2² = 1 where the tangent plane is parallel to the…

A: By see this solution

Q: Find the equation of the plane tangent to and the line (in symmetric form) normal to the ellipsoid…

A: Given:   x2+ 4y2 +8z2 = 48 Point : ( -2 , 3 , -1)

Q: At what point on the ellipsoid 2x^2 + y^2 + z^2 = 1 is the tangent plane parallel to the plane x + y…

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Q: Try to sketch by hand the curve of intersection of the parabolic cylinder y = x2 and the top half of…

A: Given that the curve of intersection of the parabolic cylindery=x2 and the top half of the ellipsoid…

Q: I am having trouble solving this.

A: To find the area of the overlap between the interior of the ellipses given below.

Q: Find a point on the ellipsoid 3x2 + y2 + 3z2 = 1 where the tangent line is parallel to the plane…

A: Given: The equation of ellipsoid is 3x2+y2+3z2=1 and the equation of the plane is -12x+2y+6z=0.…

Q: Find the radius R, of curvature to the hyperbola y = x + 3x² – x³ at the point x = 0 given that R =…

A: To find the radius R, of curvature to the given hyperbola at point x = 0.