(b) The points (2, 2, +3) are on this quadric surface. Using a distance formula, de- termine which point is closer to the plane y +z = 3? Show all necessary work to receive full credit.

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A: First we will find intersection point of the surfaces and than evaluate the slop of tangent.

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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: What is the distance between the point A(2,5,1) and the plane x + 2y +2z +1=0 ? Answer:

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Q: Fin He ara at tHe surface af the portion oF Hae Plane 2= 5-2X -9y

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A: We know the general equation of ellipsoid with center at origin (h,k,l) is, We know the general…

Q: A crate weighs 720 lb and is hung by three ropes attached to a steel ring at A such that the top…

A: Given that crate weight w=720lb  h=43, a=30in, b=49in, c=7.5 in Now drawing the free body diagram of…

Q: Find the distance (d) from the point (– 6, – 8, – 7) to the plane 5x – 2y + 2z = 25. - d =

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Q: Identify the surface 2x² + 4y? – 1=0. A. An elliptic cylinder. B.Ahyperbolic cylinder. OC. None of…

A: We will solve the problem

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Q: |Consider the sphere (x – 5)² + (y – 4)² + (z – 3)² = 25 (a) Does the sphere intersect each of the…

A: Sphere

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Q: dentify the surfaces of the following equations by converting them into equations in the Cartesian…

A: The given data is: To identify the surfaces: z2=4+4r2

Q: Prove that the locus of the point of intersection of two tangents to the parabola y? = 4ax, which…

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Q: The plane 6x + 8y + 60z = 700 intersects th of the highest and lowest points or coordinates

A: Given that the plane           6x+8y+60z=700  and the cone                            z2=x2+y2

Q: Find the point Q symmetric to the point P (1; 3; —4) with respect to the plane 3x+y-2z=0

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Q: Let S be the quadric with equation 36x² – 4y? – 9z2 – 36x = 0 - - (a) Classify the graph of S. (b)…

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Q: Qz:for fig shown, find the plane using algebric methode ל

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Q: H-w) find thi surf ace area for the Dlane 6x+44-22= 14 if this plane in the finst octant? S-A = |…

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A: It is required to find the equation of the revolution generated by revolving the given plane about…

Q: A solid has circular base of radius 20 cm. Find the volume of the solid if every plane section…

A: Given: The base of solid: Circle with radius, r = 20 cmTo find; Volume of solid (V) for every plane…

Q: 5. Calculate the distance between the point (3, 1, -2) and the plane 2x + y-2+1. O 10 o -10 V14 O 10…

A: The equation of the plane is  2x+y-z+1 = 0 The point is x0,y0,z0 =3,1,-2 To evaluate : The distance…

Q: What is the highest point on the ellipse that is the intersection of the plane z +y+ 2z = 2 and the…

A: I am going to solve the given problem by using the Lagrange's Multiplier method to get the highest…

Q: Find the distance between the point and the plane. 19. (0,0,0) and 2x+3y+z=12

A: As there are multiple questions, the first one (19) is solved here.

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A: The given equations is x2+z2=4

Q: True or False (iv) The line joining the Sun to a planet sweeps out equal areas in equal times. (v)…

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Q: d the distance between the point (2, -4, 3) and the plane 5x – 2y + z = 10

A:

Q: In each part, find an equation of the sphere with center (2, −1, −3) and satisfying the given…

A: Given that: Centre of sphere = (2, -1, -3)

Q: Find parametrizations The portion of the sphere x2 + y2 + z2 = 36 between the planes z =-3 and z =…

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Q: 4x? + у? - 327 25 3z2 = 25

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Q: Find the equations of planes that just touch the sphere (x−5)^2+(y−3)^2+(z−1)^2=9 and are parallel…

A: Solution  Given (x−5)^2+(y−3)^2+(z−1)^2=9 (a)  Parallel to the  xy-plane:   ( z-1)2= 9   z - 1= | 3…

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Q: Verify that the two planes are parallel, and find the distance between the planes. (Round your…

A: Using distance formula between parallel planes

Q: Find equetion of Hhe parabole farmm an I with focus zt (3,0) and divectrix x=-3

A: Focus =  F= (3,0)  Directrix - x =-3  i.e. x+3=0

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.