Find an equation of the sphere with center (1, -8, 3) and radius 5. (x – r- 1)² + (y + 8)² + (z – 3)² = 25 Use an equation to describe its intersection with each of the coordinate planes. (If the sphere does not intersect with the plane, enter DNE.) intersection with xy-plane (x – 1)² + (y + 8)² = 16 intersection with xz-plane (x – 1)² + (z – 3)² = -39 (y + 8)² + (x – 3)²: intersection with yz-plane

Q: Find the equation of the plane containing the line of intersection of the two planes z+y+z+5=0 and…

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Q: 13. Find an equation of the sphere with center (-3, 2, 5) and radius 4. What is the intersection of…

A: Topic = Geometry

Q: Find the distance between the point (1, 0, 2) and the plane 2x – 3y + 6z = 6.

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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 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: 2. Find the equation of the sphere with the given conditions: (a) center at (1, – 2, – 4) and its…

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Q: Find an equation of the surface of revolution by revolving the plane curve 3y = v(9- [(x-1)] ^2)…

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Q: Find the point on the sphere (x - 1)² +y² + (z + 9)² = 9 nearest to a. the xy-plane. b. the point…

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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 an equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the point…

A: To find the equation of the plane that is parallel to the plane x + 5y−z + 8 = 0 and contains the…

Q: Find parametrizations The portion of the plane 4x + 2y + 4z = 12 that lies above the square 0<=…

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Q: Determine the general equation of the plane 2 passing through the point P(-1,4, 5) and parallel to…

A: Follow the procedure given below.

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: Determine the center-radius form of the equation of a sphere which circumscribes two externally…

A: If center of sphere is (u,v,w) and radius is R then equation of sphere can be written as…

Q: Determine the general equation of the plane Ω passing through the point P(1,−4,−5) and parallel to…

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Q: Find the distance between the point (0, 1, 2) and the plane 3x - 2y + 6z = 6.

A: Using Distance from point to plane formula,

Q: Find an equation of the plane. The plane through the point (5, –1, –6) and parallel to the plane 5x…

A: Given point is (5,-1,-6) and plane is 5x-y-z=3 find the equation of the plane which is parallel to…

Q: Find an equation of the plane through the given point and parallel to the given plane. origin 2x -…

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

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Q: plane

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Q: 1. Find an equation for the set of points whose distance from the plane z =8 is twice the distance…

A: SOLUTION-

Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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Q: Determine the general equation of the plane 2 passing through the point P(1, -4, –5) and parallel to…

A: Given problem:- Determine the general equation of the plane π passing through the point P(1, -4,-5)…

Q: Find an equation for the plane through the point (3, 4, −4) and parallel to the plane defined by 4x…

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Q: Find an equation of the plane containing the point (2,1,-1) and parallel to the plane 3x – y + 2z =…

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Q: Find the distance between the point (2, 0, 1) and the plane 2x - 3y + 6z = 6.

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

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Q: Find a parametric representation for the surface. The part of the hyperboloid 5x2 – 5y2 – z² = 5…

A: Given, equation of surface is

Q: A line with parametric equations x = 10 + 2s, y = 5 + s, z = 2, seR, intersects a sphere with the…

A: The solution of given problem as follows :

Q: 2-The distance between the point (2,3,1) and the plane 5x – 2y – 4z = 0 А- 0, В- 6.7, C- V45. is

A: Here, the distance between the given plane and point is zero. Because, the point is on the plane.

Q: 1. Find the point of intersection of the plane 3x+4y-2z=13 and the line given by parametric…

A: Given :  The equation of plane is 3x + 4y - 2z = 13. Parametric equation of the line is x = 1 +…

Q: Find parametric equations of the line of intersection of the two planes. 9x + 8y - 9z = -3, -7x -…

A: According to the problem, we have

Q: The ellipsoid 2x2 + 3y2 + z2 = 30 intersects the plane y = 1 in an ellipse. Find parametric…

A: First I have found the equation of tangent and then the parametric equation.

Q: 4) Find the distance from the point (1, 2, – 1) to the plane 2x+y- 2z = 1.

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Q: Find the center and radius of the sphere. x² + y² + z² - 16y = 0 center (х, у, г) 3D radius

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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

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: Find the equation of the line tangent to (a) The parabola z = 2x2 - 3y2, y = 1 at the point…

A: To Find: The equation of the line tangent to: (a) The parabola z = 2x2 - 3y2, y = 1 at the point…

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 an equation of the plane. The plane through the point  (8, −3, −3)  and parallel to the plane…

A: We know that two parallel planes have same direction ratios(i.e. the coefficients of x,y and z…

Q: Find a parametric representation for the surface. The part of the hyperboloid 5x2 − 5y2 − z2 = 5…

A: 5x2 - 5y2 - z2 = 5 (Given)5x2 = 5 + 5y2 + z2  x2 = 5 + 5y2 + z25   x = 5 + 5y2 + z25

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

A: Topic:- geometry

Q: Find a parametric representation for the surface. The part of the hyperboloid 9x2 – 9y2 – z2 = 9…

A: Let u and v be two parameters for the given surface. Since the part of the surface lies in front of…

Q: Find an equation of the plane. The plane through the point (7, −2, −7) and parallel to the plane 9x…

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Q: A line with parametric equations r = 10 + 2s, y = 5 + 5,2 = 2, sER, intersects a sphere with the…

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Q: 16. Find an equation of the plane through the point (1, 1, –2) and parallel to the plane 3r – z =

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Q: Find an equation of the plane. The plane through the point (7, –2, –8) and parallel to the plane 6x…

A: We will solve the following.

Q: The plane x + y + 2z = 20 intersects the paraboloid z = x² + y² in an ellipse. Find the points on…

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Q: Find the distance between the point (1, 0, 2) and the plane 2x − 3y + 6z = 6.

A: To find the distance

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.