A line with parametric equations x = 10 + 2s, y = 5 + s, z = 2, seR, intersects a sphere with the equation x² + y² + z² = 9 at the points A and B. Determine the coordinates of these points.

Q: Describe the yz-intercept of the sphere with the equation x2 + y2+z2 - 2x+ 10z +5 = 0

A: The given equation of sphere is: x2+y2+z2-2x+10z+5=0

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: Consider the paraboloid given by the equation z = x^2 + y^2. Find the coordinates of the vertex and…

A: A paraboloid is a quadric surface that has exactly one axis of symmetry and no center. The given…

Q: Find the distance between the skew lines with parametric equations x = 1 + t, y = 2 + 6t, z = 2t,…

A: The distance from a point P(x1,y1,z1) to a plane  is

Q: The type of coordinate system that allows you to locate any point in space by using X, Y and Z…

A: The type of coordinate system that allows you to locate any point in Space by using X ,Y and Z…

Q: A city is described parametrically by the equation r = (ai + bj+ck) + svi + tv₂ where v₁ = 3i+j+ k…

A:

Q: Write the equation of the sphere with centre at ( 0,0,0) and radius = 2

A: The center of the sphere is:(h, k, j)=(0, 0, 0)The radius of the sphere is:r=2

Q: 1. Find the equation (formula) of a sphere with radius r and center C(h, k, 1) and show that x² + y²…

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Q: Convert each of the following points in rectangular coordinate system into points in cylindrical…

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Q: 2 y² - x² = 9 a) Sketch the graph of the equations in three dimensions and identify the surfaces.

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Q: Find the intercepts of the plane 4x+y+10z=40 . Write your answers as points (a,b,c) where a,b and c…

A: Given equation of the plane is 4x+y+10z=40. We have to find different intercepts.

Q: 91 a) Find an equation of the sphere with center (1,-3,-5) and tangent to xz-plane.

A:

Q: What is the equation for a sphere centered at the point (4,-3,-7) with a radius of 5.

A: The general equation for a sphere in three dimensions is given by (x - h)^2 + (y - k)^2 + (z - l)^2…

Q: a) Find an equation of the sphere with center (1.-3,-5) and tangent to xz-plane.

A:

Q: Find the equations for the spheres whose center is (7, -1, 5) and radius is 2.

A: To find: The equation of sphere whose centre and radius given. Given: The centre of sphere is 7,-1,5…

Q: Write the equation of a sphere of radius 3 in all three coordinates--cartesian, cylindrical, and…

A: It is given that the radius of sphere is 3 .We have to find the equation of sphere in all three…

Q: Determine the line of intersection of the two planes: x+y-z-2=0 and 2x-y+3z-1=0. Write the…

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Q: (r – 1)? + (y + 2)² + (z – 1)² = 49

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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,…

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.