What points in the xy-plane satisfy the equations and inequalities in Exercises 11–12? Draw a figure for each exercise. 11. (9x2 + 4y2 - 36)(4x2 + 9y2 - 16) <=0 12. (9x2 + 4y2 - 36)(4x2 + 9y2 - 16) > 0

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: 5) s how that the line af intersection f the Planes X+24-22= 5 and 5x-2y-73D0 is Parallel to theline…

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Q: 10) Find the equation of the line of the intersection of the planes 2x+3y+7z+2=D0, x+2y-3z+5=D0.

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Q: -1 and Determine an equation of the line of intersection of the planes 2x – y + 3z x + 4y – z = 2

A: I

Q: 13. Find the distance between the two given parallel planes. x+y-3z = 4 x+y-3z=12

A: Given that:

Q: Find the null space associated with the equations: 2x+z+w = 0 7x-6y-z-w-v= 0 -5x+4y+w = 0 (Needless…

A: NOTE: Refresh your page if you can't see any equations. . system Ax=0 is the matrix A is

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: Find symmetric equations for the line of intersection of the planes. 2 3x - y - 7, 2- Sx + 2y - 8 O…

A: Given:- Planes 1 z= 3x-y-z-7 Plane 2 z=5x+2y-8 To find:- Find symmetric equations for the line of…

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: 10) Find the equation of the line of the intersection of the planes 2x+3y+ 7z+23D0, x+2y-3z+ 5-0.

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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: 4) Find the equation of the line of the intersection of the planes -2x+3y+7z+2=0, x+2y-3z+5=0.

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Q: Find an equation for the set of points P(x, y) in a plane the sum of whose distances from two fixed…

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Q: Find the line of intersection between the two planes x+2y-z = 5 and x-4y+z=3

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Q: 30 0= +시 +씨 2 |and 3x-y-z=3 -8/

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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: find the lineof interseetion of the plane -2x + 79 -2= 24 given by 3x t6y-52=-3 the plane

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

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: 9. Determine the number of points of intersection for the planes: ₁:3x-6y + 12z - 6= 0 and ₂: 2x -…

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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: 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: Describe the set of points in 3-space defined by the equations x? + y² + z2 - 8z = 9, x = 3. %3D

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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: Q Use Lagrange multipliers to tind the maximum an Ċ minimnm valnes and Points (x ) at which they…

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

A: Given that z=10-x2-y2 and x+2y+3z=0 Find the point which is farthest from the plane.

Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: Consider the set of points in space whose coordinates satisfy the given pairs of equations. x2 + y2…

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

A: We will solve the problem

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: 4) Find the equation of the line of the intersection of the planes -2xr+3y+7z+2=0, x+2y-3z+5=0.

A: We have two equations in three variables. To find the line of intersection of these planes, we fix…

Q: What is the shortest distance from the point (4, 0, 5) to the sphere (x-1)2 + (y+2)2+2 = 367? %D O…

A: topic - shortest distance between point and sphere

Q: Find the coordinates of the intersection point of the lines x_1 + 3x_2 = 3 and −2x_1 + 4x_2 = 1 in…

A: Solved below

Q: Describe the set of points that satisfy  x2 + y2 + z2 - 2x - 4y + 6z = 2

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Q: Use Lagrange multipliers to find the point on the plane x − 2y + 3z = 6 that is closest to the point…

A: First note that ,          if (x,y,z) be any point on tha plane x-2y + 3z = 6 then distance between…

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: 10. Is there any value of k that will make the planes kx + 2y-2kz + 3 = 0 and x-2ky + 5z = 0…

A: Two planes are perpendicular iff their normal vectors are orthogonal

Q: Find the line of intersection of the planes x + 7y + z = 9 and x − 5y + 4z = 15

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Q: give a geometric description of the set of points inspace whose coordinates satisfy the given pairs…

A: Given that, x2+z2=4y=0

Q: a.Find the maximum value of w = xyz on the line of intersection of the two planes x + y + z = 40 and…

A: Given Data The equation is w=xyz. The first equation of plane is x + y + z = 40. The second equation…

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: 21. Determine an equation for the line of intersection of the following planes: 3x + 2y+ 5z = 4 and…

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is the intersection point of the main axis. In an ellipse graph, the center of the axis is the midpoint of the line segment connecting the foci. The major axis is the line section that runs through the ellipse's foci, while the minor axis runs through the middle and is perpendicular to the major axis.. The ellipse has two endpoints on the major axis which are known as the vertices (in plural), vertex in the singular. The equation of the major axis is 2a, the equation of the minor is 2b and the distance between the major axis and minor axis is 2c. The semi-major axis has a length of a and the semi-minor axis has a length of b. The ellipse's vertices are determined by the elliptical orbit's equation and graph.