This is for calculus 3.

Please be neat and show all works that support calculations! Thank you in advance!

1 1. The hyperboloid 5.22 1:2 y2 = 1 consists of two \"sheets\" (i.e., there's two halves, and they're separate; try plotting the equation}. Each sheet can have its own set of tangent planes. Find the points on the hyperboloid Where the two planes, each tangent to one sheet of the hyperboloid, meet at right angles. Find the local extrema of the function at, 3;) = e_(c(m)+5m(yn and test for which are max, min, or neither. Find the shortest distance between the surface z = x2 + y and the plane x ty - z = 4