13. The equation of the sphere if one of its diameters has endpoints (1, 2, 4) and (-1,4,0) is given by (x – a)² + (y – b)² + (z – c)² = r². Then the values of a,b, c, r² , respectivelly, are -1, 4, 0, 24 1, 2, 4, 6

Q: 3. Rectangle PORS with vertices P(5, 15). Q(15, 15). R(15, 10), and S(5, 10): A- 4/5 4. Rhombus WXYZ…

A: Plot the given points and its scaled version

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: -1 and Determine an equation of the line of intersection of the planes 2x – y + 3z x + 4y – z = 2

A: I

Q: 3. Find the shortest distance between parallel planes 2x - 3y + z = 4 and 4x -6y + 2z = 5.

A: Given equation of planes: 2x-3y+z=4 and 4x-6y+2z=5. To find: Shortest distance between the parallel…

Q: 4 Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0, z+x3=0,…

A: Find the four vertices of the tetrahedron.  Making four equation.  Then write it in matrix form.…

Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Let's find lowest and highest temperature by using langrange multipliers.

Q: close

A:

Q: 5.4. F(х, у, 2) 2³), M is the outer surface of the sphere x² + y² + z² = a². %3D

A:

Q: Find the point on the sphere  x2+y2+z2=900 that is farthest from the point (−19,−8,11).

A:

Q: Find an equation of the largest sphere that passes through the point (-1, 1,4) and is such that each…

A: Find the equation of sphere.

Q: Find an equation of the sphere that passes through the origin and whose center is (-10, 10, 5). O A.…

A: To find:-   Equation of the sphere that passes through the origin and whose center is (-10, 10, 5).

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: 4) Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0,…

A:

Q: Find the equations of the sphere through the circle x + y +2 =1, 2x+ 4y+5z= 6 and touches the plane…

A:

Q: For planes 2x + y - z = 2 and 2x + 3y + 5z = 4

A:

Q: The equation of the sphere with center (4,-2, 9) that touches that -axis is OA. (x – 4)* + (y + 2)*…

A:

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: The distance from the point S(7, 7, -6) to the plane 2x + 11y + 10z = 9

A: option C 2215 is correct detailed solution is given below

Q: If a bug walks on the sphere x^2 + y^2 + z^2 − 4x + 4y + 4z + 3 = 0 how close and how far can it get…

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 the line of intersection of the given planes. 3x + 2y + z = ~ 1 and 2x - y + 4z = 5

A: Given: 3x+2y+z=−1                                                      ...(i)2x−y+4z=5…

Q: 4. How many solutions are there between the plane P₁: (x, y, z) = (4, −3,−1) + s(1, -3,1) + t(2,4,…

A: Plane and line

Q: Find the point on the plane 2x + y + 4z = 5 that is closest to the point P(4, 3, 5). (x, y, z) =…

A: We are given a plane 2x + y +4z = 5, and we are asked to find the co-ordinates of the point on the…

Q: Find the point at which the line 7(t) = (5, – 3, - 6) + t( – 2, - 8, 6) intersects the xz plane.

A:

Q: A point moves in the (x, y) plane on the line 2x+ 3y −4 = 0. Where will it be when the sum of the…

A: We have to find a point from where the sum of square of its distances from 1,0 and -1,0 is smallest.

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 for the sphere centered at (2, 2, –2) and passing through (2, 2, 3). 1. x² + y + z²…

A: Given center is (2,2,-2) and the point is (2,2,3)We know the equation of sphere is…

Q: Find an equation of the sphere that passes through the origin and whose center is (-6, – 4, 12). OA.…

A:

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

A:

Q: Find the line of intersection of the given planes. 4x + y – z = 0 and 2x - y + 3z = 4 y = 2 + t 2

A:

Q: The center of the sphere whose one of its diameters has end points P;(1,3, –1) and P2(2,-2,1) is |…

A: Given that the endpoints of the diameter of the sphere are P11, 3, -1, P22, -2, 1 To find its…

Q: Find the line of intersection of the planes 2x – y + z = 2 and x + 2y – 4z = 1

A:

Q: Find the point on the sphere x^2 + y^2 + z^2 = 8 that is closest to the point P(2, 1, 1)

A:

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

A:

Q: Find the equation of the sphere if one of its diameters has endpoints (-5, -5, 1) and (-3, -1, 7)…

A:

Q: 9- Suppose T degrees is the temperature at any point on the sphere x² + y² + z² = 4 and T = 50x²yz.…

A: The temperature is

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

A:

Q: The equation of the sphere with center (7,-3, 1) that touches that y-axis is OA. :-7° + (y +3)* +…

A:

Q: what is the equation of the plane perpendicular to the intersection line of the x-2y+2z= 3  and…

A:

Q: 2. Find the equation of the line that is parallel to the intersection of planes 12, 2x-8y + z = 0…

A:

Q: 1. Determine the point of intersection of the line and the plane if it exists. π: 7x+y+ 5z = 0 x-4…

A:

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: Find the point on the sphere x²+y²+z²=4489 that is farthest from the point (18,-20,18).

A:

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: For planes 2x + y - z = 2 and 2x + 3y + 5z = 4.

A:

Q: 13–16 Show that the equation represents a sphere, and find its center and radius. 13. х2 + у? + z? —…

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.