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: Assume the equation of a parabola and a line are given by y = x² + 4x and y=x+4, respectively.…

A: To find out the intersection points of the given parabola and the line.

Q: The plane through the points (-4,-8,-1), (8,3,5), (7,8,6) has equation Ax + By + Cz= D. If A = - 19…

A: Since plane passes through the given points therefore

Q: Find the equation of a sphere whose center is on line 5y+2z=0=2x-3y and passes through point…

A:

Q: The plane through the points (-1,-2,-2), (-5,-3,2), (-5,2,7) has equation Ax + By + Cz = D. If A = -…

A: A = -25 B = 20 C = -20 D= 25  For detail....go through the solution.... You can solve this problem…

Q: 5. Find the standard form equation of a sphere that has a diameter with endpoints (3, -2, 4) and (7,…

A: Given : The end points of a diameter of a sphere are  (3, -2, 4) and (7, 1, 4). To find : We have to…

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

A:

Q: 2. Write the symmetric equation of a line through the points (0, 2,8) and (3,-3, 4). Find where this…

A:

Q: Determines the Cartesian equation of the plan that is parallel to the plan 2x - 3y + z - 1=0 and…

A: We have to find the equation that is parallel to the plane 2x-3y+z-1=0. Also plane passes through…

Q: What are the intersection points of the parabola given by the equation y = x2 – 9 and the line given…

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.