1. Find the distance from the center of the sphere given by (x-2)² +(y+2)²+(z-1)² = 4 to the point (1, 2, 4).

Q: Sketch the section of the surface at y = 0. 2x + z = 3 4 -8 -6 -4 2/4 -2 6 8 -6 -8- 6. AM -8 -6 -4-…

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Q: What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z = 3 -…

A: To find the equation for the largest ball centered at (0, 0, 1) that can fit in the below equation…

Q: If a parametric surface given by r₁ (u, v) = f(u, v)i + g(u, v)j + h(u, v)k and -2 ≤ u ≤ 2, -3 ≤ v ≤…

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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: Determine the points on the surface y2+z2−x=8 that are closer to the origin.

A: Consider the given surface. y2+z2−x=8z2=8−y2+xf(x,y)=8−y2+x

Q: 2. Find the equation of the sphere with the given conditions: (a) center at (1, – 2, – 4) and its…

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Q: Find the center and radius of the sphere X² + y² + z² −2x−4y + 8z + 17 = 0

A: Given: Equation of a sphere is x2+y2+z2-2x-4y+8z+17=0. To find the center and radius of the sphere.…

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: 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 area of that portion of the surface of the paraboloid x² + y² = 4z included between…

A: Here we need to find area between given plane and x*x + y*y = 4z

Q: Find the standard equation of the sphere with the given characteristi Center: (-1, -9, 7) Radius: 9…

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Q: Describe in words the level curves of the top half of the sphere x2 + y2 + z2 = 1.

A: Top half of the sphere will be a hemisphere.

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: Sketch the surfaces CYLINDERS z = y2 - 1

A: We need to sketch the surface formed by the function

Q: Find the area of the part of the sphere x2 + y2 + z2 = 4z that lies inside the paraboloid z = x2 +…

A: Given, x2+y2+z2=4z  and  z=x2+y2 Equation of the sphere and paraboloid in cylindrical coordinates is…

Q: Find the center C and the radius a for the sphere 1. 3x2 + 3y2 + 3z2 + 2y - 2z = 9 2. x2 + y2 + z2 -…

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

Q: Find the center C and the radius a for the spheres 2x2 + 2y2 + 2z2 + x + y + z = 9

A: General equation of a sphere, x2+y2+z2+2ux+2vy+2wz+d=0 Centre of sphere = -u, -v, -w Radius of…

Q: Find an equation for the sphere with center at (-7,8,0) and radius = 9 O x2 + y? O x2 + y2 + z- -…

A: We have to find

Q: Consider the sphere x² + y² + z² = 9. Please find the equation of the plane tangent to this sphere…

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Q: Find the center and the radius of the sphere. 2 + y2 + z2 + 4x + 5z = 0

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Q: Find the area of the portion of the surface z = 8x+4y that lies above the triangular region with…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Sketch the xy-trace of the sphere whose equation is (x−3)2 +(y−2)2 +(z+4)2 =52.

A: We can find the xy trace by setting z = 0 in the original equation.

Q: Find the equation of the sphere with center at (-3, 2, 4)and of radius 6. A (x-3)2+ (y – 2) ²+ (z-…

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Q: 10. Find the area of the portion of the sphere x2 + y² + z² = 16 between the planes %3D z=1, z=2.

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Q: Find the center C and the radius a for the spheres x2 + y2 + z2 - 4x + 6y - 10z = 11

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Q: Sketch the section of the surface at y = 0. 1 + x² + y² Z = 4 -8 -6 -4 -2 4 4 6. 4 -8 -6 -4 -2 2. 4…

A: Given data is: To sketch the surface at y=0 z=1+x2+y2

Q: Find the center C and the radius a for the spheres (x + 2)2 + y2 + (z - 2)2 = 8

A: We have to find the center C and radius for the given sphere equation: x-22+y2+z-22=8 We know that…

Q: Find the points on the sphere at which the minimum and maximum distances between the sphere…

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Q: Find the center and the radius of the sphere that has the given x2 + y2 + z2 + 10x – 7y + 2z + 26 =…

A: Given a equation of the sphere , x2+y2+z2+10x-7y+2z+26=0 To fin the center and the radius of the…

Q: Find the center and radius of the sphere. x2 + y2 + z2 - 18y + 12z + 36 = 0 (x, y, z) = ( 0,9, – 6…

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Q: Find the center C and the radius a for the spheres 3x2 + 3y2 + 3z2 + 2y - 2z = 9

A: Given: The equation of sphere as 3x2+3y2+3z2+2y-2z=9, To find: The center C and radius a for the…

Q: Find the equation for the sphere centered M(2,-3,2) tangent to the D:6x-3y+2z-11=0 plane

A: we have to find the equation for the sphere centered 2,-3,2 and tangent to the plane 6x-3y+2z-11=0.

Q: 2.5 What is the distance between two parallel hyperplanes {r E R" | a"x = b1} and {r E R" | a"x =…

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Q: 28. Show that the ellipsoid 2x² + 3y² + z² = 9 and the sphere %3D x? + y? + z? - 6x – 8y – 8z + 24 =…

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Q: 3.4.8 Show that the sphere x² + y² + z² = 1, z ≥ 0. JJ,z²dS=, where S is the surface of

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Q: Which is the equation of a sphere with a center at (1,0,-2) with a volume of 36(pi)(u^3)? a.…

A: We first defined the equation of sphere and centre,volume . Using this formula we have equation (a)…

Q: 2.5 What is the distance between two parallel hyperplanes {x E R" | a"x = b} and {x E R" | a"x =…

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Q: Sketch the section of the surface at y = 0. 4 2 -2 -6 -4 -6 -4 4 6. -61

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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 radius of the sphere x^2+4x+y^2 -2y+z^2-7=0

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Q: Find the equation of the sphere of radius 7 centered at (3, 5, 3). O (x – 3) + (y– 5 + (z - 31 = 7 O…

A: Let's find.

Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = √2/2.

A: Given equation of sphere is    x2+y2+z2=1     And the equation of plane is  z=22=12 But we know that…

Q: 3. Show that every sphere through the circle x2 +y-2ax+r²=0, z=0 cuts orthogonally every sphere…

A: This is a co-ordinate geometry problem

Q: Prove that the surface of the given equation is an ellipsoid. Hence, determine its center. 9x +4y…

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Q: 6. The part of the surface z = 1 + 3x + 2y² that lies above the triangle with vertices (0, 0), (0,…

A: Given: A surface z=1+3x+2y2 and vertices of triangle (0, 0), (0, 1) and (2, 1). To find: Area of…

Q: Find the extreme values of ƒ(x, y, z) = x2yz + 1 on the intersection of the plane z = 1 with the…

A: consider the following equations  f(x,y,z)=x2yz+1                                  (1)h(x,y,z)=z-1…

Q: Find the center and the radius of the sphere. x^2+y^2+z^2-6x+3z=0

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Q: Find the center and radius of the sphere. 2 4x + 4y + 4z + x + y+z= 25

A: Topic = Sphere

Q: Find the sphere’s center and radius. x2 + y2 + z2 + 10z = 0

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Q: Find the point lying on the intersection of the plane  x + (.5)y + (.25)z = 0  and the sphere  x2…

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Angles in Circles

Angles within a circle are feasible to create with the help of different properties of the circle such as radii, tangents, and chords. The radius is the distance from the center of the circle to the circumference of the circle. A tangent is a line made perpendicular to the radius through its endpoint placed on the circle as well as the line drawn at right angles to a tangent across the point of contact when the circle passes through the center of the circle. The chord is a line segment with its endpoints on the circle. A secant line or secant is the infinite extension of the chord.

Arcs in Circles

A circular arc is the arc of a circle formed by two distinct points. It is a section or segment of the circumference of a circle. A straight line passing through the center connecting the two distinct ends of the arc is termed a semi-circular arc.