The equation of the sphere centered at C(h, k, 1) ad radius r is given by (x - h)² + (y-k)² + (z-1)² = r² Find the center and radius of the sphere with equation x²++y²+z²-4x +2y +6z 11 =0 (HINT: Use completing the

Q: quation of the hyperb

A: Given,      z=-16

Q: find the center and the radius of the sphere x^2+y^2+z^2+2x-5z=0

A: Equation of the sphere is  (x-a)² + ( y-b)2+ (z-c)2 = r2  Where (a,b,c) are the centre and r be the…

Q: Find an equation of the sphere with center (-5, 2, 7) and radius 7. (x +5)2 + (y – 2)² + (z – 7)² =…

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Q: Find the point on the sphere x²+y2+z2=2304 that is farthest from the point (1,-18,-27).

A: d  = x-12+y+182+z+272d2 = x-12+y+182+z+272fx, y, z = x-12+y+182+z+272subject to the constraintgx,…

Q: Find parametric equations for the line of intersection of the planes x + 2y + 3z = 4 and 5x + 6y +…

A: Given: x+2y+3z=4   and  5x+6y+7z=8To obtain the parrametric…

Q: Find the distance from the point (2, –1, 5) to the plane 3x + 2y – 2z – 7 = 0.

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Q: a) Find the distance between the points (7,0,1) and (-5,4,2). b) Find the center and radius of the…

A: According to our guidelines we can answer only three subparts ,or first question and rest can be…

Q: Q1) Find the centers and radius of the spheres for: (x - V2) + (y- v2) + (z + V2) = 2 * (+ })' • (-…

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Q: Find the distance from the point (2, 2, 3) to the plane 2x + 3y + 5z = 0.

A: Formula of distance of a point from a plane:

Q: The surface S formed by the point P(x,y,z) such that the distance from P to the point A(1.0,-1) is…

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Q: Among all the points on the graph of z = 11-x² - y? that lie above the plane x+ 5y + 6z = 0, find…

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Q: The equation of plane through the origin and parallel to the plane 2x+ 5y – 4z = 8 is 2x + 5y – 4z =…

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Q: Find the point on the sphere x2+y2+z²=900 that is farthest from the point (14,-5,-1).

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

Q: The equation of the sphere with center (2,-3, 10) that touches that y-axis is OA (x- 2)° + (y +3)* +…

A: Solution is given below:

Q: find the distance from the point to the plane. (0, 0, 0), 3x + 2y + 6z = 6

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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: 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: Find the center and the radius of the sphere. x2+y2+z2+3x+3z=

A: See the details solution in below

Q: Find the point on the plane 4x+7y+8z−19=0 closest to the point (−2​,1​,3​).

A: Given,

Q: Q1. Find the equation of sphere with center (1, 2,-1) passing through the point (-1, 2, 1).

A:

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 with center (-5, 4, 6) and radius 8. (x + 5)² + (y – 4)² + (z – 6)? =…

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Q: c) [. The intersection of the sphere B and the xz-plane is (x - 2)² + (z + 1)² 2)² + (z + 1)² = 9.…

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Q: Find an equation of the surface consisting of all points P(r, y, z) that are twice as far from the…

A: To find an equation of the surface whose all points are twice as far from the plane z=-4 as from the…

Q: The plane containing the point (-7,-1,0) and parallel to the plane 5x + 8y – 2z Ax+By+ Cz = D. If A…

A: Given the plane containing the point (-7,-1,0) and parallel to the plane 5x+8y-2z=-5 has the…

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 largest sphere contained in the cube determined by the planes x = 0, x = 8,…

A: given the planes:

Q: Find the point on the sphere x²+y2+z²=1225 that is farthest from the point (6,9,24).

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Q: Find the center and radius of the sphere x2 + y2 + z2 + 3x - 4z + 1 = 0.

A: The given equation is x2 + y2 + z2 + 3x - 4z + 1 = 0.   The Standard Equation for the Sphere of…

Q: Find the canonical or standard equation of the sphere, if it exists. 2x² +2y² + 2z² – 4x+12y–16z+6=0…

A: To write the canonical or standard equation of the below sphere. 2x2+2y2+2z2−4x+12y−16z+6=0

Q: Find an equation of the sphere concentric with the sphere x^2 + y^2 + z^2 + 4x + 2y − 6z + 10 = 0…

A: Topic = Geometry

Q: 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…

A: Given equation of the sphereis x-22+y+22+z-12=4So center of the sphere be 2,-2,1and the given…

Q: Find the point on the sphere x2 + y2 + z2 = 4 farthest from the point (1, -1, 1).

A:

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

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

Q: Choose the surface or graph described by the given equation x2+ y2+ z2- 2x- 3y+ 4z -25=0 Has no…

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Q: Find the center and radius of sphere x^2+y^2+z^2-20z =0.

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Q: Find the intersection of the two planes with equations 3(x – 1) + 2y + (z + 1) = 0 and (x – 1) + 8y…

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Q: Find the intersection of the two planes with equations 3(x - 1) + 2y + (z + 1) = 0 and (x - 1) + 5y…

A: Dear,as per company guidelines we can answer only one question at a time, kindly post other question…

Q: The equation of the sphere with center (3,-10, 9) that touches that y-axis is OA. (r-3)2+ (y 10)+…

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Q: 9. Find the center and radius of the sphere given by 3x + 3y? + 3z2 = 10 + 6y + 12z.

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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: #5: 12(x')? + 3(y')² = 48 , rotated 30° from its position in the xy-plane

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Q: Part 1 of 8 By re-ordering the sphere equation, we have z- 100 - - y, We can then parameterize this…

A: We have to parameterize the given equation z2 = 100 - x2 - y2.

Q: b. the distance from B(0, –1, 0) to the plane with equation 2x + y + 2z – 8 = 0

A: Topic:- geometry

Q: Find the point on the sphere  x2+y2+z2=7056 that is farthest from the point (5,−15,−2)

A: The given question has been solved in detail

Q: 2 Find the point on the sphere x² + y² + z² = 16 farthest from the point (-1,-1,1). The point is…

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Q: Find the intersection of the two planes with equations 3(x - 1) + 2y + (z + 1) = 0 and (x - 1) + 8y…

A: The equation of the given planes are  3(x - 1) +2y + (z +1)=0...... (1) (x - 1) + 8y - (z +1)=…

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

A:

Q: 5. Cakculate the distance between the point (3. 1. -2) and the plane 2x + y - z+1-0 O 10 /14 O -10…

A: Find the distance between point and plane?  Value of k for det A= -4

Q: 5. Find the distance from the point (4, -3, 6) to the plane *-2y+z=1

A:

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.