A(n)............ is the collection of all points in the plane the sum of whose distances from two fixed points is a constant

Q: 2. An is a set of points (x, y) in a plane such that the sum of the distances between (x, y) and two…

A: We know that, The sum of distances to any point on the ellipse x,y from the two foci c,0 and -c,0 is…

Q: 6. The distance between a point x E R and a nonempty set A CR is defined by d(x, A) = inf {|x – y| :…

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Q: Consider the collection of all points of the form – 2w] 3w w Express this collection as the span of…

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Q: Consider the reglon bounded by the graphs of y- and y- VE

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Q: a. Show that Ø, R E T. (by definition of Topology)

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Q: Suppose that l is a line. Let H be one of the two half-planes bounded by l. Give a proof that l U H…

A: Answer is mentioned below

Q: Calculate the are bounded by the curves: C. y = e2x and x - 2y + 5 = 0

A: Introduction: The formula of the area between the curves y=f(x) and y=g(x) is given by,…

Q: Bounded by the planes z= x, y =x, x+y=2 and z= 0

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Q: Let XC Rn convex. Prove that x is an extreme point of X if and only if the set Cis convex, where X =…

A: Let X⊂ℝn be convex . To prove: x is an extreme point of X if and only if the set C is convex, where…

Q: Let the function f is defined on the disk x² + y? < 1, then f has a critical point somewhere on this…

A:

Q: Let M be the region bounded by the parabola y = r² and the line y = x + 2. %3D 6. y = r +2 5. 2,4)…

A: Given that, The shaded region bounded by the parabola y=x2 and the line y=x+2 is M.   And the region…

Q: Find the absolute maximum and minimum values of the function f(x; y) = x+y-xy: on the set D, where D…

A: Given, the function is f(x, y) = x + y -xy on the set D and D is the closed triangular region with…

Q: Show that R is not compact.

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Q: Let A₁, A2, A3,..., A,, are n points in a plane whose co are (x₁, y₁), (x2, y2),..., (x, y),…

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Q: Each nonempty can be represented as the convex hull of its extreme points. --------

A: Each of the nonempty compact convex set can be represented as the convex hull of its extreme point.

Q: 28. The locus of the points z such that /z 3/ = 2 is A. x² + y = 4 C. x* + y - 6y + 5 = 0 D. x+ y-…

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

Q: 5. Evaluate f (x²zdx – yx²dy + 3dz) where C is the boundary of the triangle with vertices (0,0, 0),…

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Q: Let F = (z, 2x, y) and C is the straight segment from (0,0,0) to (1,2,3). Then ,F dř = %3D %3D

A: Given,                                   F→(x, y, z)=z, 2x, yand C is the straight segment from (0,…

Q: Provide inequalities for r and that precisely describe the region in the xy-plane bounded by the…

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Q: 3. lind Analytic function in, the disk 7z-11<1 whose veal part

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Q: Let f(x, y, z) = x²y°z – xyz², and compute: (a)

A: In this question we will use basic of vector  calculus i.e gradient of any function and curl of…

Q: The value of the integral (inage 1). where C is the closed curve 4x2 + 5y2= 7, 3x + 2y − 9z = 5.

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Q: Show that the function f(x, y, 2) = (x² + y² + 2e**)4 is strictly convex on R³.

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Q: Which of the following sets of inequalitites describes the region consisting of all points outside…

A: Given that, Region consisting of all points outside or an a sphere of radius 4 centered at the…

Q: Prove Theorem (AT )T = A

A: Given: Theorem, ATT=A.

Q: If the function f is defined on the disk x2 + y² < 1, then f has a critical point somewhere on this…

A:

Q: 28. Bounded by the planes z = x, y = x, x + y = 2, and z

A: Solution:-

Q: 1. 2. The area bounded by y = = -(x - 1)² + 4 , and the lines x =1, y = 2, and y = 4 rotated about…

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Q: For the qutegradsSEddy tringle Over the bounded by -0,4=0 and *+y=l-

A: We have to find the integral  ∬e2x+3y dx dy   over the region R bounded by curves: x=0, y=0, x+y=1

Q: 1. Let F(x) = x. Compute the first five points on the orbit of 1/2.

A: Given:    F(x) = x2   First five points on the orbit of (1/2)

Q: Use the Heine-Borel theorem to show that every closed and bounded interval [a, b] with the absolute…

A: Compact Set: A collection A of subsets of space X is said to be cover X or covering of X if the…

Q: Consider the collection of all points of the form y – 2w 3w Express this collection as the span of…

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Q: Find the surfaces on which the function u = 2 (x2 + y²)/z is constar

A: Since u is a constant so, x2+y2z=4a , where a is an arbitrary constant.

Q: A (σ,ρ) regulated source is served at a network link with transmission rate C >ρ. Show, using…

A: Given: Here the given is at a network link with transmission rate C &gt;, a (,) regulated source is…

Q: Consider the following subsets of real plane R termine with graph: Arcwise connected A = ((x,y): 0 ≤…

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Q: 6. The distance between a point x ER and a nonempty set A CR is defined by d(x, A) = inf {\x – y| :…

A: In this question, we have to prove that d(x,A)=0 iff x belong in closer(A)

Q: 3. Let D be the region bounded by the parabola y= -3 and the line y=1.F

A: The region is bounded by the curves given by: y=x2-3      and      y=1

Q: 3. (a) Show that under the mapping w = 1/z, all circles and straight lines in the =-plane are…

A: (a) We have to show under the mapping w = 1/z, all circles and straight lines in the z plane are…

Q: 1. Show that if & is a function from a nonempty compact metric space X to itself such that d(@(x),…

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Q: Determine whether the work done along the path C is positive, negative, or zero. /c/ zero negative…

A: For calculating the work done from the field we will have to see the direction of both vector field…

Q: ind the absolufe maximum and minimum values Of the set D. a. f(x,y) = x² + y² – 2x, D is the closed…

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Q: consider the map given by F(x)=1-x² discuss the charactristics of the orbits starting at x=0

A: As per the question we are given the following map : F(x) = 1 - x2 And we have to explain the…

Q: Use greens theorem to evaluate line interal (x2y)dx+y2dy),where c is the closed path formed be y=x…

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Q: Determine whether the work done along the path C is positive, negative, or zero. negative positive…

A: Consider the provided graph, Determine whether the work is done along the path c is positive…

Q: Sketch the graph of the convex hull of S. In R, let S =. :0sx<3

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Q: The graph of f(x,y)=y2-x2 on XYZ space has a saddle point (a,b) if... choice: (choose one correct…

A: Objective is to find the condition for saddle point

Q: 4. Show that the distance between the two points z1 and z2 in an Argand diagram is |z1 – z2). In…

A: (6) z-1=2 Given that:The points z=x+iy satisfies the condition z-1=2 The complex number z=x+iy…

Q: Describe geometrically the set of points z satisfying the following condition:|z−2i|=3 .

A: The general form of a complex number is given by z=x+iy, where x,y are two real numbers and i=-1.…

Q: Compute the convolution y(n) = x(n) * h(n) , Where x(n) = {1,1,0,1,1} and h(n) = {1,-2,-3,4} , Using…

A: Given: Given convolution expression is Y(n)=x(n)*h(n) x(n)={1,1,0,1,1} h(n)={1,-2,-3,4}

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.