5. Find the coordinates of the points on the cross sectional curve of the intersection of the cone 2 = √x² + y² and the plane x + 2y + 3z = 3 that have maximum and minimum distance from the xy-plane (see the sketch below). Hint: Use the Lagrange Multipliers method. cone intersection curve plane xy-plane

Q: Determine the geometric location of the points in R3 that equidistant from the plane y = 3 and the…

A: This is question of 3d geometry and locus.

Q: Suppose XY has coordinates X( -2, 5) and Y(3, -9). What are the coordinates for the midpoint of XY?

A: To find the Midpoint of the line.

Q: Find the distance from the point (2, 2, 3) to the plane 2x + 3y + 5z = 0.

A: Formula of distance of a point from a plane:

Q: Find the distance between the parallel planes 4x – 3y + 12z = 12 and 4x — Зу + 12z 36.

A: In this problem we have to find distance between two parallel planes.

Q: If (x1, yı) and (x2, y2) are distinct points in the plane, show that y 1 1 =0 X1 x2 y2 is the…

A: If (x1, y1) and (x2, y2) are distinct points in the plane, to show that  xy1x1y11x2y21 =0 is the…

Q: Alt X 6. Find the distance of the point P = (2,3,-1) to the plane 2x - 3y + z = 1.

A: