Excercise 76 Let 0 < ) < 1 be a given real number. Using Cartesian coordinate system prove that the transformation (axial affinity) P(т, у) њ Р(т, Лy) sends any circle to an ellipse. Conclude that the area of an ellipse is abn .

Q: Question: find the hyperbolic distance between (0,10) and (3,4)

A: Formula Used: Hyperbolic distance between two points (x1,y1) and (x2,y2) is  distHx1,y1 , x2,y2 =…

Q: Show that the triangle with vertices A(7,8), B(1, 20), C(1, 10) is an isosceles right ti plane model…

A: Given: To explain the given statement as follows, In the upper half-plane model for hyperbolic…

Q: find a parametrization of the curve. The line passing through (1, 0, 4) and (4, 1, 2)

A: Given: A line is passing through the points 1, 0, 4 and 4, 1, 2.

Q: 3. Find parametric equations for the graph of a circle centered at (-3,1) and radius 3.

A: Let's find parametric equations for the graph.

Q: If a point, P1=[10,10,10], will be rotated by 60 degree about the Z-axis, find the final position…

A: Solution ) suppose P1 [ x1 y1 , z1] is rotated about z axis so new point P2 [ x2 , y2 , z2 ] is…

Q: Describe the graph of the relation determined by   Indicate the direction in which the curve is…

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Q: Use the parametric equations of an ellipse, x = 5 cos(0), y = 3 sin(0), 0 ≤0≤2π, to find the area…

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Q: Draw a two-dimensional figure that could be rotated using a vertical axis of rotation to give the…

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Q: 5/1f the three points A ( are collinear then

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Q: c{(a,b), r} circle of center (a, b) and radius r 2 2 (x-a)² + (x−b)² = r² Convert to polar…

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Q: Mathematically show what planes the face centered cubic cell allows x-ray reflections from.

A: Here we have to show mathematically what planes the face centered cubic cell allows x-ray…

Q: One polar coordinate representation for the rectangular point (2, – 2) is (2/2.* (2/3. - :) -(2/3. -…

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Q: Find an equation of the line in parametric form that passes through the vertex of the paraboloid…

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Q: Express the conics in polar coordinates.

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Q: Determine the coordinate of a 3D point (100.0, 29.0, -79.5) after rotating 60° across Y-axis, given…

A: Given:                       point: A100.0,29.0,-79.5                Rotation: θ = 60° across…

Q: Consider the line r in the space that passes through points A = (1, 3, −1) and B = (3, −1, 1).…

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Q: Use projections to find the distance from the point P(1,1,—1) to the plane 2x+6y-3z=1. Please…

A: find the distance from the point to plane.

Q: Q3/ For the given vertices A, B, C and D of the parallelogram, Find the angle at B and the polar…

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Q: Q4\ find a polar equation for the circle x² + (y - 3)² = 9

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Q: nd the Cartesian and the polar form of 7e

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Q: △ABC△ABC has vertices A(0,4), B(6,-1), and C(3,7). What are the coordinates of C' when the triangle…

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Q: Is a triange with the verticies A(7,1) B(0,4) and C(-4,-8) a right triangle yes or no?

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Q: %3D Line L and Line m are parallel lines that have been rotated 180°. The resulting images are show…

A: Please see the answer in Step 2.

Q: The coordinates of quadrilateral ABCD are as follows: A = (3,0), B = (7,1), C = (6,-4), and D=…

A: Given dataThe coordinates of quadrilateral ABCD are,

Q: 1 Consider AABC. YA 8 -6 -8 4 A --8--6-4-221416181 B # Paralelogram PQRS has verticas PXC-4), and S…

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Q: Find a polar equation for a parabola that has its focus at the originand whose directrix is the line…

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Q: Can duality concepts be extended to non-Euclidean geometries? How?

A: Yes, duality concepts can indeed be extended to non-Euclidean geometries, although the specific…

Q: AB has endpoints at (-9, 12) and (3, -6). Its transformation A'B' has endpoints at (-3, 4) and (1,…

A: Endpoints of AB  A (-9,12) B(3,-6)   Endpoints of A'B' A"(-3,4) B'(1,-2)

Q: (2,5). Find the angle between the vector, in degrees. Let ā = ( − 1, 4) and 6 = Question Help: Video…

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Q: Triangle ABC is reflected across the y-axis to form the image A’B’C’. Triangle A’B’C’ is then…

A: Triangle ABC is reflected across the y-axis to form the image A'B'C'. Triangle A'B'C' is then…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.