Which of the following correctly depicts the sphere given by the equation: x2 + (y - 2)2 + (z - 2)2 = 4?

Q: Show that the equation represents a sphere, and find its center and radius: x? + y? + z2 – 2x – 4y +…

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Q: Show that the equation represents a sphere, and find its center and radius: 2x2+2y2+2z2=8x-24z+1

A: To show that the equation represents a sphere, and find its center and radius: 2x2+2y2+2z2=8x-24z+1

Q: Find the radius and center of each sphere. [Hint: Complete the square in each variable.] x2 + y2 +…

A: The general equation of the sphere is given as x-x02+y-y02+z-z02=r2. Here, the center of the sphere…

Q: Find the center and radius of a sphere with the equation: 8x + 4z = 1 − 2x^2 + 20y − 2y^2 − 2z^2.

A: Given the equation of the sphere 8x+4z=1-2x2+20y-2y2-2z2

Q: Find the standard equation of all circles having center at a focus of 52 7(x+2)? (y-3)2 = 1 39 and…

A: Let's find.

Q: 7. x2 +y? +14x- 12y + 4 0 %3D Center : (_and radius:

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Choose the equation that represents the graph of the quadric surface below 3. 21 O z = 4 - 5y2-92 O=…

A: From graph we see that the quadric surface represents a paraboloid whose axis is y-axis Here 1st…

Q: 5. Show that the equation represents a sphere, and find its center and radius: x²+y? + z2 – 8x – 10y…

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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 coordinates of the foci for the following hyperbola. (x – 1)? (y + 1)? 1 64 16

A: I am going to solve the given problem by comparing it with the standard form of hyperbola whose…

Q: Direction is provided for the sphere problem

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Q: 1. Find the center and radius of the given equation of the sphere. x + y +z´ - 4x+ 6z+12=0

A: Given: The equation of sphere is x2+y2+z2-4x+6z+12=0.

Q: Complete the square to write the following equation as standard equation of a sphere and find center…

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Q: Write the equation of the sphere in standard form. 9x? + 9y? + 9z2 = 36x – 12y – 24

A: The givne equation of the sphere is 9x2+9y2+9z2=36x-12y-24

Q: x² + + =1 y2 9. 4

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Q: c) Find the center and radius of the sphere whose equation is

A: Given, we need to evaluate the norm of the following vectors. i=<-1,2,4>ii=-i+7j

Q: Find the center and radius of the sphere with equation (x + 1)² + (y + 2)² + (z – 2)² = 4 Center:…

A: Explanation of the solution is given below...

Q: Find b and c, given that the parabola y = x2 + bx + c passes through (0, 5) and (3, 23).

A: (0,5) means when x=0 then y=5. similarly, (3,23) means when x=3 , then y=23.

Q: 2.Express the equation in standard form and indicate the center and radius, if a circle exists. a.…

A: Part a,Given,            x2+y2-10x-14y-7=0We know that,          The general equation of the circle…

Q: 5. Show that the equation represents a sphere, and find its center and radius:…

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Q: The figure on the right shows a rhombus centered at the origin, with YR= 8p and PQ - 8s. What are…

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Q: 8: Which one of the following conics is a parabola? 22 + y + 5 = 4æ B 222 + y? = 4x +4 4r – 9y? +…

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Q: c) Find the center and radius of the sphere whose equation is x² + y² + z² + 10x + 4y + 2z – 19 = 0

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Q: State whether the given equation defines an elliptic paraboloid, a hyperbolic paraboloid, or an…

A: 3x2-7y2=z On simplification, we get ⇒z=x213-y217⇒z=x2132-y2172⇒z=x132-y172

Q: Which of the following equations of parabolas has its vertex at (1, 2)? O y= 12 + 2x + 3 O y= r² +…

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Q: Show that the equation represents a sphere, and find its center and radius: x²+y² + z² – 8x + 6y +…

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Q: x² +y? + z² + 8x – y + 5z = 2

A: solution

Q: Find the center and radius of the sphere with equation (x + 2)2 + (y - 3)2 + (z + 6)² = 16 Center:…

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Q: 3. Find the center and radius of the sphere having the equation: x²-4x+y² +8y+z² – 2z=4

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Q: For Exercise, an equation of a hyperbola is given. Determine whether the transverse axis is…

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Q: What is the equation of circle in standard form? x²+4x+y²-6y=23 O A. (x-2)2+(y+3)²=6 O c…

A: A circle is the locus of points in two-dimensional space which are equidistant from a fixed point.…

Q: Find the equation of the sphere

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Q: For the sphere with equation (x - 1) + (y + 2) + (z + 4) = 36, find a) the center. b) the length of…

A: The given sphere equation is x-12+y+22+z+42=36.

Q: Find the radius and centre of the sphere x + y + – 4x + 2y-6z-11=0.

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Q: What is the second coordinate of the center of the sphere of the equation below?…

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Q: The equation a? + y? = 9 in 3-space is circle. Select one: OTrue OFalse

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Q: c) Find the center and radius of the sphere whose equation is x2 + y? + z? + 10x + 4y + 2z – 19 = 0

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Q: Evaluate y ds, where C is the parabola r (3t2, 3t), for 0 <t< 1. %3D

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Q: Find the centre and radius of the sphere determined by the equation x' +y° +(z - 2) = 16 %3D

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Q: Find an equation of the sphere that passes through the origin and whose center is (-6, – 3, – 2). O…

A: We know that,  General equation of sphere is given by, (x-a)²+(y-b)²+(z-c)²= R² where, R is the…

Q: Find the center and radius of the sphere with equation (x + 3)² + (y + 1)² + (z − 1)² = 64 Center:…

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Q: Write the sphere equation x^2 + y^2 + z^2 + 2x - 2y -2z = 33 in standard form, and hence find the…

A: x2 + y2 + z2 + 2x -2y - 2z = 33To Find: The center and the radius of the sphere.

Q: c) Find the center and radius of the sphere whose equation is x² + y? + z? + 10x + 4y + 2z - 19 = 0

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Q: The equation of the shown hyperbola is given by Fou Fou Select one: (x– 1)? _ (v+2}? , 9. 5 (y+2}? _…

A: Explanation of the answer is as follows

Q: The surface of equation – +- 1 is: 16 A sphere O A cone O An ellipsoid || + 이닙

A: We can explain it as below using the concept of three dimensional geometry.

Q: Given the equation, (x-h+v-k)² =r?,what are the coordanates of the center? The coordinates of the…

A: Answer and explanation is given below....

Q: The equation of the hyperbola whose foci are (-2,0) and (2,0) and length of transverse axis is 2 is…

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Q: The equation x +4y² = 4 in three-dimensional space is an equation of which surface? O Ellipse O…

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Q: Which conic section is represented by the equation 9x2+4y2=36

A: Simple conic section problem......

Q: For Exercise, determine whether the transverse axis and foci of the hyperbola are on the x-axis or…

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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.