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 .

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A: Centroid of a Triangle Definition: For a two-dimensional shape “triangle,” the centroid is obtained…

Q: Figure ABCD is a trapezoid. Which sequence of transformations will carry figure ABCD onto itself?…

A: Given that a trapezium ABCD. Find which of the given sequence of transformations will carry figure…

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A: The 3 rigid transformations are,

Q: 9. Consider the regular octagon below with center at the origin and a vertex at (4, 0) Describe one…

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Q: A' B' C' C Construct Transform The two triangles to the left are equilateral triangles. Are they…

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Q: Use Green's theorem to compute the area of an ellipse given by the equation + 1.

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Q: In the Cartesian plane, graph the sets of points whose polar coordinates satisfy the inequalities 0…

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Q: Create one model or figure for a Poinrcare Upper Half-Plane model of hyperbolic geometry.

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Q: Show that the image of the hyperbola x² - y² = 1 is the transiscate p² = cos24.

A: Introduction: An hyperbola is another significant conic section. It has Cartesian as well as polar…

Q: Use a projection to derive a formula for the distance from a point (x,y) to the line ax+by=c, where…

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Q: 10. True or false: a linear fractional transform maps ellipses to ellipses, parabolas or hyperbolas.

A: Solution

Q: Which degenerate conic is formed when a double cone is sliced through the apex by a plane parallel…

A: Given question:- Which degenerate conic section is formed when a double cone is sliced through the…

Q: 57. Use a change of variables to prove that the area of the ellipse with equation (-) + ) : -1 is…

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Q: 80. Give an example of the reflective property of a parabola.

A: We have to give some examples of the reflective property of a parabola.

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Q: Consider the figure. Which rotation about its center will result in the regular pentagon being…

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Q: Using the property of Re z and im z to show that the hyperbola x2 z2 + (z)² = 2 = 1 can be written…

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Q: Create one model or figure for a Klein-Beltrami model of hyperbolic geometry.

A: To create: One figure for a Klein-Beltrami model of hyperbolic geometry.

Q: 10. Consider the regular octagon below with center at the origin and a vertex at (4, 0). -3 -2 -1 3…

A: Given, Octagon  whose centre at the origin and one vertes at (4,0)

Q: By integration, show that : 8. The area of an ellipse with semi axes a and b is A = nab.

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Q: Figure ABCD is a trapezoid. Which sequence of transformations will carry figure ABCD onto itself?…

A: In this question we have to find a figure that is symmetric to the original figure.

Q: If the coordinates of the ends of a focal chord of the parabola y²=4ax and (x,,y,) and (x,.y;) then…

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Q: Find the projection of v

A: Here v→=2i^-2j^    and w→=-3i^+j^

Q: Graph the image of trapezoid RSTU after a rotation 180° counterclockwise around the origin. 104 5

A: Given that:

Q: Name the coordinates of Point A after a rotation 90 degrees counterclockwise. 124 10 12 10 4. 10 12…

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Q: Find the surface of the regular pyramid.

A:

Q: Find the center, foci, vertices, asymptotes, and radius, as appropriate, of the conic sections in…

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Q: Find an equivalent quadratic form by using a diagonal rotation, (by the principle axis theorem. I…

A: Given: Q=2x2+4y2+6yz-4z2=80

Q: (b) Describe fully a single transformation that would map triangle VAC onto triangle V"A"C".

A:

Q: Write a two-column proof showing that triangle ABC is congruent to triangle ADE. Then, describe…

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Q: 9) If figure A is rotated 90 counterclockwise around the origin, which figure is the image of A7…

A: Counter clockwise means rotated in anti clockwise direction.

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Q: 25. Prove analytically that the four diagonals joining opposite vertices of a rectangular…

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Q: Exer. 1-14: Find the vertices and foci of the ellipse. Sketch its graph, showing the foci. 9. 2. 25…

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Q: 9. Consider the regular octagon below with center at the origin and a vertex at (4, 0). Describe one…

A: Consider a regular octagon centered at origin.

Q: 2. Determine the equation of the conics shown below

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Q: Exer. 1-14: Find the vertices and foci of the ellipse. Sketch its graph, showing the foci. 21 25 16…

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Q: Using the property of Re z and Im z to show that the hyperbola x2 – y? = 1 can be written as: z² +…

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Q: Q5: Use the necessary transformation to generate Figure3 (polygon) from Figure2 (the two parallel…

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Q: Change from rectangular to spherical cooordinates (√3, 1, 2√3)

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Q: Q9. Draw a sketch of a hypersphere in four dimensions.

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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.