Consider the sphere (x − 4)² + (y − 3)² + (z − 5)² = 25 (a) Does the sphere intersect each of the following planes at zero points, at one point, at two points, in a line, or in a circle? The sphere intersects the xz-plane? The sphere intersects the xy-plane? The sphere intersects the yz-plane? (b) Does the sphere intersect each of the following coordinate axes at zero points, at one point, at two points, or in a line? The sphere intersects the y-axis? The sphere intersects the z-axis? The sphere intersects the x-axis? at zero points

Q: Write the equation (in standard form) of the parabolic arch formed in the foundation of the bridge…

A: here we have to find  the equation (in standard form) of the parabolic arch formed in the foundation…

Q: Write the equation of a sphere that has a center at C(2, 5,-3) and contains points D(4, 1, 1) on the…

A: Given Data: The centre of the sphere is: C(h, j, l)=C(2, 5, -3) The point at the edge of the sphere…

Q: ind the standard equation of the sphere  with diameter and end points below (6,-1,-2), (4,11,12)

A:

Q: = 6x² - 3y² + 1 in a: By setting one variable constant, find a plane that intersects the graph of z…

A:

Q: Find an equation for the plane containing the three points (0, 1, -1), (1,0,1), and (2, 1, 0). Where…

A:

Q: Find an equation of the plane that crosses the x-axis at 3, the y-axis at 2, and the z-axis at 5.

A:

Q: Find the equations of planes that just touch the sphere (x - 5)² + (y − 4)² + (z − 2)² = 25 and are…

A:

Q: The following equation represents a sphere: x² + y² + z² = 1. Which one of the following is the…

A:

Q: Find the equations of the osculating circles of the parabola y = 3(x – 2)2 at the points (2,0)

A:

Q: nts, in a line, or in a circle? sphere intersects the xz-plane ? sphere intersects the yz-plane ?

A: Introduction: If (a, b, c) is the sphere's center, r is the radius, and x, y, and z are the…

Q: (222) Determine the x-, y- and z-intercepts of the plane 3x-8y-8z +24=0

A:

Q: Arrange the parabolas represented by the equations according to the positions of their foci on the…

A: The standard form of a parabola is  (x – h)2 = a(y – k) where (h, k) is the vertex.

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

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…