What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure for each exercise. 11. (x2/9) + ( y2/16) <=1 12. (x2/9) - ( y2/16)<= 1

Q: Of all the points on the graph of z = 10 - x^2 - y^2 that lie above the plane x + 2y + 3z = 0, what…

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Q: 2:- find the line of interSection o f the plane -2x + 73 - 2324 given by 3x t6y-52=-3 f the plane

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Q: What is the y-coordinate of any point in the xz-plane?

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Q: 3. Find the shortest distance between parallel planes 2x - 3y + z = 4 and 4x -6y + 2z = 5.

A: Given equation of planes: 2x-3y+z=4 and 4x-6y+2z=5. To find: Shortest distance between the parallel…

Q: Use calculus of variation to derive the shortest line (equation) that joining points (x,y,z) =…

A: Given plane -   7x + 2y + 3z = 7 Parametric equation will be =  (1 - t, 0- 2t, 0 - t) Hence,

Q: 13) Find the points of intersecti on of the parabola and the line. y=2x^2-3x-1 and y=x+5

A: Equate the equations with each other and solve for x to find the point of intersection .

Q: What is the length of the latus rectum of the curve x2=-12

A: Answer

Q: Find the distance between the parallel planes P and P2 P: 2x-y+ 3z 6 = 0 P2: 6x - 3y+9z+ 6 = 0 8 *…

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Q: 2) The distance between the parallel planes ax + by + cz + d1 = 0 and |d1-d2| ax+by+cz + d2 = 0 is…

A: We find required equations of plane parallel to given plane.

Q: 9. Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

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Q: 5. (a) Find an equation for the line of intersection between the planes r+3y-z = 2 and 2x – y+2z =…

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Q: Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

A: Let's find lowest and highest temperature by using langrange multipliers.

Q: 8) Determine an equation of a line that passes through the point P (5,-2,3) and is parallel to the…

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Q: c) Find the minimum distance from the point (4,0,6) to the plane x- y +2 = 3

A: The solution is given below. .

Q: Among all the points on the graph of z = 11-x² - y? that lie above the plane x+ 5y + 6z = 0, find…

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Q: In the xy-plane, how many points on the curve y² + x² = 3 – xy have horizontal or vertical tangent…

A: The given curve is  y2+x2=3-xy

Q: Find the points of intersection of the pairs of curves in Exercises 31-38. 31. y = 2x²5x-6, y = 3x +…

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Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: To find the distance from the point 0,1,1 to the line of intersection of the planes:…

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

A: As per our guidelines we are supposed to answer only one question at a time. So I am solving the…

Q: 7. Show that the equation of the plane that has x-intercept a, y-intercept b, and z-intercept c…

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Q: What is the shortest distance from the point (4,0, 5) to the sphere (x – 1)2 + (y + 2)2 + z² = 36?…

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Q: A(n)________ is the collection of points in the plane the difference of whose distances from two…

A: The given statement is "A(n)________ is the collection of points in the plane the difference of…

Q: Determine shortest distance of the line 2x-3y-8 to the vertex of the curve x2 - 4a 4y +4 0. O 2 O…

A: We have given a line ,and find the shortest distance from vertex of parabola to line.

Q: Q4:Show if the line (x = 5y +17, y+z-2= 0) lies in the plane 3x-41y-26z +1 = 0 or no ? Where does…

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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: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: Use equation of plane

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: Find an equation for the set of all points equidistant from the point (0, 0, 2) and the xy-plane.

A: Let any such point is given by (x,y,z)(x,y,z) is z units away from the xy plane.

Q: 12 Which point is equidistant from the planes T1:- 2x +y- 2z + 3 = 0 and 73: - 2x + y- 2z + 21 = 0?…

A: Option B is correct :- (explained below)

Q: A point moves in the (x, y) plane on the line 2x+ 3y −4 = 0. Where will it be when the sum of the…

A: We have to find a point from where the sum of square of its distances from 1,0 and -1,0 is smallest.

Q: 24) By using Lagrange multiplier find a point in the plane x+2y+3z=13 nearest to the point (1,1,1)

A: We have to find a point in the plane x+2y+3z=13 nearest to the point 1,1,1 by using Lagrange…

Q: Give a geometric description of the set of points whose coordinates satisfy the given conditions.…

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Q: 3. Use LaGrange multipliers to find the point on the plane 2r - y+4z = 10 that is closest to the…

A: Use Lagrange method to find point

Q: 5/ Find the point at which the line through points P1(2. 3, 0) and P2 (-6. -3, 12) meets the plane…

A: Consider the points  P12,3,0 and P2−6,−3,12

Q: Find equation of Plane teter mined by the Lines Li. X = t-29 y = 2t+3 Z= +4 and Lz! X…

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Q: 4 - Find an equation of the Planc perpendicular to each of the planes X-y +2=0 and 2x ty - 4z -5 =0…

A: A detailed solution is given below

Q: 4) Find line of intersection for 2 planes.  2x-3y+z=5 -x+2y+3z=2

A: We will solve the problem

Q: ii) Prove that the straight line y = x is the curve giving the shortest distance between the points…

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Q: What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure…

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Q: Suppose there are two lines in the xy-plane in R^2.  These two lines could intersect at a single…

A: let the lines be                              y=m1x+c1y=m2x+c2 given that lines are intersecting in…

Q: Find an equation of the curve in the xy-plane that passes through the point (2, 3) and has, at every…

A: integration

Q: Q:- find of the the line of interscetion plane given by 3X +6y -S2=-3 f the plane -2x + 79 -2=24

A: 3x+6y-5z+3=0 -2x+7y-z-24=0 Let z=t 3x +6y = 5t-3 -2x+7y = t+24

Q: Findauihtvectorhermat to thesuFace X Y +X2=1 et the Point (-1,1,1)

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Q: What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure…

A: Since you have submitted two questions, we\'ll answer the first question. For the second question…

Q: Charlie and Alexandra are running around a circular track with radius 60 meters. Charlie started at…

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Q: Find a point with z = 2 on the intersection line of the planes x + y + 3z = 6 and x - y + z= 4 .…

A: Given, equation of planes x+y+3z=6x-y+z=4

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

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Q: 1. F = [2², -x², 0], S the rectangle with vertices (0, 0, 0), (1, 0, 0), (0, 4, 4), (1, 4, 4)

A: As given that,  F→=z2i^-x2j^+0k^ Calculating curl F,…

Q: Find the minimum distance from the point to the surface z = √4 - 2x - 2y. (Hint: To simplify the…

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