the distance to the x axis is:√(y2+ z2)
the distance to the yz-plane is: x
2x =√(y2+ z2)
4x2=y2+ z2
x2=y2/4+ z2/4
is the equation of a cone centered on the x axis.
Find an equation for the plane consisting of all points that are equidistant from the points (-4, 4, 1) and (2, 6, 5).
rty. I 5. [16 pointsj Consider the function f(x, y,z) Let S denote the level surface consisting of all points in space such that f(,y,z)-4, and let P- (2,-2,1), which is on S. a) Calculate Vf. b) Determine the maximum value of Daf(P), where u is any unit vector at P c) Find the angle between Vfp and PO, where O denotes the origin. d) Find an equation for the tangent plane to S at P rty. I 5. [16...
Problem 1. (33 Points) (a) Consider the following: Are these two planes parallel? If not, find the parametric equation of their line of intersection (b) Describe the set of all points P = (x, y, z) such that the distance from P to the y-axis is twice the distance from P to the zz-plane. (c) Describe the set of all points P (r, y, 2) such that the distance from P to the plane x + 5y-4z = 1 equals...
3.(10 points) Find an equation of the tangent plane to the surface (a) z = xe” at the point P(1,0,1). (6) sin xz - 4 cos yz = 4 at the point P(11,1,1).
16x2-y2 + 42. 16-0. Identify and sketch the surface EXAMPLE 7 Dividing by -16, we first put the equation into standard form: SOLUTION z2 16 4 Comparing this equation with equations of quadratic surfaces, we see that it represents a hyperboloid of two sheets the only difference being that in this case the axis of the hyperboloid is the y-axis The traces in the xy and yz-planes are the hyperbolas 16 and z2 =1 4 x=0. 16 The surface has...
Describe in words the surface whose equation is given the plane perpendicular to the xy-plane passing through y X, where x 2 0 3 the top half of the right circular cone with vertex at the origin and axis the positive z-axis the base of the right circular cone with vertex at the origin and axis the positive z-axis 3 x, where x 2 0 the plane perpendicular to the xz-plane passing through z the plane perpendicular to the yz-plane...
Find an equation of the plane tangent to the following surface at the given point. yz e XZ - 21 = 0; (0,7,3) An equation of the tangent plane at (0,7,3) is = 0. Find the critical points of the following function. Use the Second Derivative Test to determine if possible whether each critical point corresponds to a local maximum local minimum, or saddle point. If the Second Derivative Test is inconclusive, determine the behavior of the function at the...
Linear Algebra 10. [10 points] Consider the plane P represented by the equation 2z+3y-2z = 0. (a) Find a basis for P. (b) Find a basis for the intersection of P with yz-plane
Find an equation of the plane tangent to the following surface at the given point. 4xy + yz + 3x2 - 32 = 0; (2,2,2) The equation of the tangent plane at (2,2,2) is = 0.
Find a formula for the distance from the point P{x,y,z) to each of the following planes. a. Find the distance from P(x,y,z) to the xy-plane. b. Find the distance from P(x,y,z) to the yz-plane. c. Find the distance from P(x,y,z) to the xz-plane. a. Choose the correct formula for the distance from the point P(x,y,z) to the xy-plane. O A. Iz OB. Mx2 + y2 OC. Vz OD. x² + y² + 2? b. Choose the correct formula for the...