4. The terminal point of v=3i-2j is (4, -4) if the initial point is (1,-2). 5. The standard equation of the sphere that satisfies the stated conditions (center (1, 0,-1); diameter-5) is (x – 1)2 + y? + (z + 1)2 = 25.

Q: Graph the quadric surfaces given by the equations in Exer- cises 41–48. y2 41. x² = y? x2 42. z2 9.…

A: As per guidelines incase of multiple questions (or) multiple sub-parts asked we are supposed to…

Q: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

A: Given S as a quadric with equation 4x^2 - (y-3)^2 + 4z^2 = 4 Find a generating curve for S (as a…

Q: 9. Find the equations of the planes that are parallel to 2.x - 2y + z = 5 such that the distance…

A: We will solve the problem.

Q: Suppose that a cylindrical container of radius r and height L is filled with a liquid with volume V…

A: Consider the given:  Express volume in terms of “h”, “r” and “w”.…

Q: What is the equations of the tangent line in the given plane 1. Tangent to the parabola z = x^2 +…

A: The given surface is:…

Q: I just need #20

A: Given,

Q: Suppose surface #1 is defined by o =45° , 0 <ps9, 0 < z< 6 and surface #2 is defined by 0 =56.3° The…

A: given:

Q: 4 Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0, z+x3=0,…

A: Find the four vertices of the tetrahedron.  Making four equation.  Then write it in matrix form.…

Q: 8. Find a parametric representation of the line through the point P(1,0,4) and perpendicular to the…

A:

Q: Consider the quadric ax2 + y2 + 4z2 + x + 6y−4z = −a−10 where a is a parameter. Find all the values…

A:

Q: 4. Graph the surface 1 = y² + z² – by first sketching at least three cross sections in each of the…

A: Graph the surface by using a 3D graphing calculator like desmos. Three cross sections in xy plane…

Q: Find an equation for the sphere with center at (-7,8,0) and radius = 9 O x2 + y? O x2 + y2 + z- -…

A: We have to find

Q: 5. Among all the points on the graph of z = 10 – x² – y² that lie above the plane r+2y +3z = 0, find…

A:

Q: Find the center and the radius of the sphere. 2 + y2 + z2 + 4x + 5z = 0

A:

Q: 4) Show that the equation of the sphere circumscribing the tetrahedron whose faces are y+z=0,…

A:

Q: The equation x² – 2x + y - 4y + z2 – 2z – 10 = 0 | | represents the equation of a sphere centered at…

A:

Q: The equation of the sphere with center (4,-2, 9) that touches that -axis is OA. (x – 4)* + (y + 2)*…

A:

Q: Find the point on the sphere x²+y²+z²=961 that is farthest from the point (19,1,–9).

A: We have to find the farthest point from the given point.

Q: делеп, 47²-9y² = 9(2²+4) -TRACE ON TY PLANE: Put 2=0. 2 4x²-9y² = 36 36 Put 346 Nas w/co x² - y² g…

A: To Sketch: the graph of  4x2-9y2=9(z2+4).

Q: 2 b) Prove that Imz=0, larg z - 41= 4, 2-ž =0, 1Z-il=1Ztil are different equations all describing…

A: If we let z=x+iy then We will show that y=0 which is the equation of real axis.

Q: Among all the points on the graph of z = 10 − x2 − y2 that lie above the plane x+ 2y + 3z= 0, find…

A: We have, z = 10 - x2 - y2 and equation of plane is , x + 2y + 3z = 0 The required point on z = 10 -…

Q: 2.2 Find the maximum and the minimum values of f(x,y,z) = 5x – 3y +7z on the sphere x +y +z = 83. 2

A: Here we find the maximum and minimum value of f(x, y, z)

Q: Find the equation of spheres passing through the circle x+y+z'-6x-2z+5 =0, y = 0 and touching the…

A:

Q: 4.1.25 Show that the largest inscribed rectangular parallelepiped x2 y? z2 1 36 on the ellipsoid is…

A: first, we proved the general case.

Q: Which of the following point is the closest point on the sphere z² + y² + z² = 4 from the point…

A: Given Equation of Sphere X2+y2+z2=4 And point (3, 1, -1)

Q: The equation of the sphere with center (9,-6, 10) that touches that -axis is OA (x - 9)? + (y +6)* +…

A: The general equation of the sphere with center (a, b, c) is given by (x-a)2 + (y-b)2 + (z-c)2 = r2…

Q: Find the equations of all spheres in R 3 of radius R = 3 passing through the point (7 ,8, 9) that…

A: To find the equation of spheres Given that, from the question  Radius R = 3  with Passing through…

Q: Find the points on the sphere at which the minimum and maximum distances between the sphere…

A:

Q: Find the center and the radius of the sphere that has the given x2 + y2 + z2 + 10x – 7y + 2z + 26 =…

A: Given a equation of the sphere , x2+y2+z2+10x-7y+2z+26=0 To fin the center and the radius of the…

Q: .2 The surface z? = 1 is a 25 - - 36 hyperboloid of one sheet. Select one: OTrue OFalse

A:

Q: Find an equation for the sphere centered at (2, 2, –2) and passing through (2, 2, 3). 1. x² + y + z²…

A: Given center is (2,2,-2) and the point is (2,2,3)We know the equation of sphere is…

Q: Find the center C and the radius a for the spheres 3x2 + 3y2 + 3z2 + 2y - 2z = 9

A: Given: The equation of sphere as 3x2+3y2+3z2+2y-2z=9, To find: The center C and radius a for the…

Q: Find the canonical or standard equation of the sphere, if it exists. 2x² +2y² + 2z² – 4x+12y–16z+6=0…

A: To write the canonical or standard equation of the below sphere. 2x2+2y2+2z2−4x+12y−16z+6=0

Q: 1. Find the distance from the center of the sphere given by (x-2)² +(y+2)²+(z-1)² = 4 to the point…

A: Given equation of the sphereis x-22+y+22+z-12=4So center of the sphere be 2,-2,1and the given…

Q: Find the point on the sphere x^2 + y^2 + z^2 = 8 that is closest to the point P(2, 1, 1)

A:

Q: Given surface A₁: x = 2√y + 1 and sphere A₂: x² + y² + z² − 16x + 6y - 4z + 76 = 0 - 1. Give the…

A:

Q: The standard equation of the sphere that has center (1,-2,1) and passing through the origin, is…

A: To find the standard equation of the sphere that has center 1, -2, 1 and passing through the origin.…

Q: The center of the sphere x² –2x+y² +z² +2z=6 is Select one: O a. None O b. (-1,0,1) O c. (2,0,-2) O…

A:

Q: A parabola has an equation of y²=2x, compute the radius of curvature at point (2, 2)

A:

Q: What kind of conic section is given by the quadratic form ? -11x,? + 84x,x2 + 24x2? = 156 Transform…

A: Given quadratic form is-11x12+84x1x2+24x22=156The above conic is determined and transformed to…

Q: The equation of the sphere with center (7,-3, 1) that touches that y-axis is OA. :-7° + (y +3)* +…

A:

Q: 12. Use Lagrange multipliers to find the point(s) on the intersection of the sphere r²+y²+z² = 16…

A:

Q: 4x? + у? - 327 25 3z2 = 25

A:

Q: Prove that using the only the form of the given equation (no graphing) that it is a paraboloid.…

A: We need to prove that the the equation: x2+z2-y4=1 is a paraboloid.

Q: 11. The equation of a sphere with center at (-3, 2, 4) and of radius 6 units is? a. x² + y² + z²…

A: Equation of sphere is (x-h)2+(y-k)2+(z-l)2=r2. Where (h, k, l) is coordinates of the center.

Q: In the 3D coordinate system, for the quadric with euqation ax2 + y2 + 4z2+x + 6y − 4z = −a − 10…

A: The quadric with equation ax2 + y2 + 4z2+x + 6y − 4z = −a − 10 where a is a parameter. We need to…

Q: The point of the sphere with equation X x²-2x +y²-4y +z²-6z+10=0 nearest to the xz-plane is 0.

A:

Q: Find an equation for the sphere with the given center and radius. Center (0, -4, -1), radius 9 O x2…

A: In this question we have to find the equation of sphere.

Q: 13–16 Show that the equation represents a sphere, and find its center and radius. 13. х2 + у? + z? —…

A: