Points A = (−5, 12, 0) and B = (13, 0, 0) are on the sphere x2 + y2 + z2 = 132. Find the distance that separates A and B, traveling on the sphere, not through it.

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: Do the points (1, 0,−1), (0, 2, 3), (−2, 1, 1), and (4, 2, 3) lie in the same plane? Justify your…

A: To check: If the points (1, 0,−1), (0, 2, 3), (−2, 1, 1), and (4, 2, 3) lie in the same plane and…

Q: t 36.(x+1) =4 2 2

A: The given equation,(y-8)22+36(x+1)2=4

Q: Given the equation (z - 13)+y? = 64, identify the center and radius. Do not enter any spaces when…

A: In this we have to tell the center and radius of circle.

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: The midpoint between the points (6, -7, -2) and(-2, 1, 4) is

A: The solution of the problem is given in the next step.

Q: Two skaters are practicing at the same time on the same rink. A coordinate grid is superimposed on…

A: please refer to the image below

Q: Explain why it is impossible to find four points on the same plane equidistant from each other.

A: Let us imagine that we have 3 points in a plane that are equidistant from each other. These points…

Q: A quadratic surface has the equation x2+2y2+2z2+2yz = 1. Write the equation in standard form.…

A: To write the quadratic surface equation \( x^2 + 2y^2 + 2z^2 + 2yz = 1 \) in standard form and…

Q: Identify the quadratic surface of the equation 6x? + 3y? + 222 + 24x – 6y – 12z + 39 = 0 Choose an…

A: Given, 6x ^ 2 + 3y ^ 2 + 2z ^ 2 + 24x - 6y - 12z + 39 = 0

Q: The midpoint of \overline{\text{AB}}AB is M(0, -4)M(0,−4). If the coordinates of AA are (-8,…

A: Given Data: The midpoint of AB¯ is: Mxm, ym=M0, -4 The coordinates of A is: Axa, ya=A-8, -7 Let The…

Q: Find the center and radius of a sphere given by equation 3x +3y² +3z? =10+6y+12z.

A: We have to find

Q: Complete the square method: Show all your work! Put x² + y² 10x + 6y 15 = 0 in center radius form.…

A:

Q: Write the standard equation for the circle of radius 2v3 and centered at point (-2, 4)

A: