Consider the equation of the following conic section. Find the symmetric matrix associated to this conic section, and diagonalize it in order to find the principal axis of the conic section. Find the rotation matrix in this case needed to change the x, y axes into the principal axis: * 2x2 − 3xy − 2y2 + 10 = 0

Q: Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic.xy − 8x − 4y…

A: We have to determine the type of conic of the given equation by performing the rotation of axes to…

Q: Performa a rotation of axes to eliminate the xy-term of the conic 9x2 +4xy+9y2-20 = 0. Identify the…

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Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

A: The given quadratic equation is: 8x2+8xy+8y2+102x+262y+31=0. To Do: Using the Principal Axes Theorem…

Q: Perform a rotation of axes to eliminate the xy-term, and sketch the graph of the conic.x2 + 2xy + y2…

A: Comparing the given equation with Ax2+Bxy+Cy2+Dx+Ey+F=0, we get, A=1, B=2, C=1, D=2, E=-2 and F=0.…

Q: Consider 13 -6v3zy+7y- 256 0. Classify the conic section and (2) calculate the angle of rotation of…

A: Given the equation of the conic section is  13x2-63xy+7y2-256=0                      (i) The general…

Q: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

A: Given quadratic equation is 10x2-18xy+10y2-45=0

Q: Rotate the coordinate axes to remove the xy- term, then identify the type of conic and sketch its…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: a) Find the vector component of L = along A = and orthogonal to L. b) Find the area of the triangle…

A: I am doing all parts of que 2.

Q: Identify the conic with th e given equa­tion and give its equation in standard form…

A: Given:  A conic of equation 3x2-4xy+3y2-282x+222y+84=0. To Find: The given conic also write it ina…

Q: y? – 4y + 4x 16 = 0 is the equation of a conic. Write the standard form of that conic. |

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Q: (b) The equation 7x2 - 3xy + 5y² + 4x - 16y- 121 = 0 represents a non-degenerate conic. (i)…

A: We have to find the type of conic of given equation

Q: (b) Find for what value of the equation 12x²+36xy + y² + 6x + 6y + 3 = 0 represents a pair of…

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Q: Find the equation of the conic in the rotated system that eliminates the cross-product term and find…

A: Given

Q: Perform a rotation of axes to eliminate the xy-term. (Use x_2 and y_2 for the rotated coordinates.)…

A: Given that, The equation of the conic is 6x2-43xy+2y2+4x+43y=0

Q: Rewrite the equation in a rotated x′y′​-system without an x′y′​-term. Use the appropriate rotation…

A: Consider the given equationx2+xy+y2-19=0.the general form of cartesian conic equation…

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: Use the Principal Axes Theorem to perform a rotation of axes to eliminate the xy-term in the…

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Q: O Reduce the equation x + 2ry +y +4 V2x - 4V2y = 0 to the standard form and hence %3D identify the…

A: The given equation is x2+2xy+y2+42x-42y=0

Q: For the equation, 9x² +8/3xy+y²-8=0, complete the following questions. a. Rewrite the equation in a…

A: The general form of a conic equation is Ax2+Bxy+Cy2+Dx+Ey+F=0, where A, B, C are not equal to 0.