Find the surface area of the part of the sphere x² + y² + z² = 16 that lies above the cone z = √√x² + y²

Q: . Use the method of completing the square to write the following equation in standard form and…

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Q: The intersection of the sphere (x-3)^2 + (x+2)^2 + (z-1)^2 = 49 with each of the coordinate planes…

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Q: Find the coordinates of the midpoint of LB if L(8,5) and B(-6,2).

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Q: Find the equation of the sphere having the circle x +y+ z2 = 9, x- 2y+ 2z = 5 as a great circle.

A: The solution is below.

Q: Find the Center and radius of the Cirele x?+y²+4X-6y -320

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Q: Find the area of the hyperbolic (geodesic) triangle with vertices (3,0), (4,0) and (5,0).

A: Let P(3,0), Q(4,0) and R(5,0) be three vertices.  It is known that the equation of hyperbolic line…

Q: Identify the quadratic surface of the equation 6x? + 3y? + 222 + 24x – 6y – 12z + 39 = 0 Choose an…

A: Given, 6x ^ 2 + 3y ^ 2 + 2z ^ 2 + 24x - 6y - 12z + 39 = 0

Q: Complete the square method: Show all your work! Put x² + y² 10x + 6y 15 = 0 in center radius form.…

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Q: Find the point on the sphere x²+y²+z²=961 that is farthest from the point (19,1,–9).

A: We have to find the farthest point from the given point.

Q: Write the quadratic surface x2-y2+4z2+2x+4y+1=0 in standard form.

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Q: find the points on the surface

A: Given, S: x2-y2+6z=0=fx,y,z where normal line to the surface is parallel to the line passing through…

Q: nts, in a line, or in a circle? sphere intersects the xz-plane ? sphere intersects the yz-plane ?

A: Introduction: If (a, b, c) is the sphere's center, r is the radius, and x, y, and z are the…

Q: Find the center of the sphere x² + y? + z? + 4x – 8z + 19 =

A: To find the center of the equation from the given equation.

Q: Find the equation of the sphere with its center at (-2, 4, 13) and tangent to 3x + 4y - 12z = 10.…

A: Given: The center of the sphere is -2, 4, 13. To Find: The equation of the sphere with center -2, 4,…

Q: Find the matrix A of the quadratic form associated with the equation. 3x2 2xy + 3y² + 8z² - 46 = 0 A…

A: The equation in the matrix form is Applying congruence operation on the matrix…

Q: Find the area of the largest rectangle that can be inscribed in the ellipse  x2/a2 + y2/b2 = 1.

A: Let (x,y) be a vertex of rectangle. Then, length of rectangle = 2x, width = 2y. Then area of…

Q: The equation of the sphere with Center (4,-1,3) and radius √5 is

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