Find an equation of the sphere that passes through the origin and whose center is (6, – 6, 3). OA. (x + 6)* + (y - 6)* + (z - 3)' = 9 OB. (x-6)? + (y+6)* + (z-3)² = 9 OC. °(x + 6)* + (y-6) + (z +3) = 9 -(y-6)* + (z+3)² = 9 OD 2 +y? +z? = 9 OE. (x - 6)* + (y+6)* + (z-3)? = 81

Q: The equation (x − 1)² + (y − 4)² + (z − 3)² = 25, - is an equation of the sphere with center C(1,4,…

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Q: Write the equation of the sphere in standard form. x2 + y2 + z2 + 12x - 4y + 4z + 35 = 0 Find its…

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Q: Find equations of the spheres with center (2, −3, 6) that touch (a) the xy-plane, (b) the yzplane,…

A: To find the equations of the spheres with center (2, −3, 6) that touch (a) the xy-plane, (b) the…

Q: Find an equation of the plane that contains the intersection points of the ellipsoid 9x? + 4y² + 9z²…

A: GIVEN : Ellipsoid 9x2 +4y2 + 9z2 = 36

Q: Find the standard equation of the sphere with the given characteristics. Center: (-1, –-2, 4)…

A: NOTE: Refresh your page if you can't see any equations. . the center is  and the radius is

Q: 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 equation of the xy-trace of the sphere. (x + 2)2 + (y + 1)2 + (z − 3)2 = 25 Sketch…

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Q: Find the equation for a hyperbola centered at (0, 0), with foci at (0, - V 52 -6) and (0, 6). y? x2…

A: Here we have to find the equation of hyperbola having a center (0,0) with foci at 0,-52 and 0,52 and…

Q: Find an equation for the sphere with the given center and radius. Center (0,0,10), radius = 2 O A. X…

A: Topic = Geometry

Q: Find the equation of the xy-trace of the sphere. (x – 2)? + (y + 4)² + (z – 6)? = 72 Sketch the…

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Q: Find the center and the radius of the sphere. x2+y2+z2+4x-5z=0

A: Comparing with standard equations of sphere,

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: 3. Determine the center and radius of the following sphere: x² + y² + z² - 2x - 4y + 8z - 15 = 0

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Q: Find an equation of the sphere that passes through the origin and whose center is (-10, 10, 5). O A.…

A: To find:-   Equation of the sphere that passes through the origin and whose center is (-10, 10, 5).

Q: Identify the surface that corresponds to the equation 3y^2 - 2x - 8z^2 = 0. O elliptic hyperboloid…

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Q: 17. Find an equation in standard form for the circle centered at (7,–2) with radius 8. A. (x – 7)² +…

A: I have appended the formula used in the solution part.

Q: Find the equations of the sphere through the circle x + y +2 =1, 2x+ 4y+5z= 6 and touches the plane…

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Q: Write the equation of the sphere in standard form. x2 + y2 + z2 + 8x - 4y + 4z + 15 = 0 Find its…

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Q: The equation of the sphere with center (4,-2, 9) that touches that -axis is OA. (x – 4)* + (y + 2)*…

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Q: 1. Give the coordinates of the center, vertices, covertices, and foci of the ellipse with the given…

A: NOTE:- AS POSTED MULTIPLE INDEPENDENT QUESTIONS, WE ARE ANSWERING ONLY FIRST QUESTIONS FOR YOU AS…

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: Match the quadric surfaces to its graph. A. y + = 4+ 4x² C. 9z + 4y = 36 + 36z² B. 42 + y? + 4z² =…

A: We have to identify which Quadratic equation corresponds to which of the given 3D graphs.

Q: Find an equation of the sphere that passes through the origin and whose center is (-10, 11, – 2).…

A: Given: Origin point : ( 0 , 0 , 0 ) Center : ( -10 , 11 , -2 )

Q: Find the equation of the sphere with center c= (0, -1, 2) and radius r= 5. O x2 + y + 1)2 + (z + 2)2…

A: Biref answer is given below.

Q: (b) Find the equation of the tangent plane to the hyperboloid r2 + 3y? – 322 = 1 at the point (1,…

A: We have to find the equation of the tangent plane to the hyperboloid x² + 3y² − 3z² = 1 at the point…

Q: Find the equation of spheres passing through the circle x+y+z'-6x-2z+5 =0, y = 0 and touching the…

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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: The equation of the sphere with center (9,-6, 10) that touches that -axis is OA (x - 9)? + (y +6)* +…

A: The general equation of the sphere with center (a, b, c) is given by (x-a)2 + (y-b)2 + (z-c)2 = r2…

Q: Find an equation of the sphere with centre in the xz-plane and passing through the points (0, 8, 0),…

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Q: Find an equation for the sphere centered at (2, 2, –2) and passing through (2, 2, 3). 1. x² + y + z²…

A: Given center is (2,2,-2) and the point is (2,2,3)We know the equation of sphere is…

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: Given surface A₁: x = 2√y + 1 and sphere A₂: x² + y² + z² − 16x + 6y - 4z + 76 = 0 - 1. Give the…

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Q: Find the equation of sphere that passes through the point (-2, -8, -2) and centered at (8, 7, 8).…

A: To find the equation of the sphere that passes through the point -2, -8, -2 and centered at 8, 7, 8.

Q: The sphere, x + y² + z? – 4y + 2z – 20 = 0, has a center at which point? (0,-2,-1) (0,2,-1) (2,1,1)…

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Q: Find the radius and center of the sphere. x2 + y² +z² - 6x + 8y – 4z = - 13 r=

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Q: Answer the following questions about the sphere whose equation is given by + y' + z – 6x + 10y = 2.…

A: Compare the given Equation with standard equation of sphere then find radius and center

Q: Consider the intersection of the ellipsoid x^2 + 2y^2 + 4z^2 = 22 with the plane x = 2.…

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Q: Find the center C and the radius a for the spheres (x - 1)2 + (y - 2)2 + (z + 1)2 = 103 + 2x + 4y -…

A: Standard equation of sphere is given as x-x12+y-y12+z-z12=r2, where x1,y1,z1 is center of sphere and…

Q: The standard equation of the sphere that has center (1,-2,1) and passing through the origin, is…

A: To find the standard equation of the sphere that has center 1, -2, 1 and passing through the origin.…

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: Consider the Equation:  x2 + y2 + z2 + 8x - 6y + 2z + 17 = 0 1. Show that the equation represents…

A: x2 + y2 + z2 + 8x - 6y + 2z + 17 = 0

Q: The equation of the sphere with center (7,-3, 1) that touches that y-axis is OA. :-7° + (y +3)* +…

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Q: Verify that the line r(t) = [1 + t, 1 - t, t] is part of the one sheeted hyperboloid x^2 + y^2 -…

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Q: Find an equation for the sphere centered at (1, -2, 3) containing the origin. V14 = x + y+ z 14 = x?…

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Q: 4x? + у? - 327 25 3z2 = 25

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

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Q: The point of the sphere with equation X x²-2x +y²-4y +z²-6z+10=0 nearest to the xz-plane is 0.

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Q: Let 11 be the surface with the equation = 2√y+1 and let 12 be the sphere with equation x²+y+z² 16x +…

A: Given data÷ Find the center and radius of the sphere   x2+y2+z2-16x+16y-4z+76=0   General form of…

Q: Find an equation for the sphere with the given center and radius. Center (0, -4, -1), radius 9 O x2…

A: In this question we have to find the equation of sphere.