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A Conic Section Is Given by the Equation 4x² $\theta$ To Find the New Equation of the Conic Section in 10xy

Question 18

Multiple Choice

A conic section is given by the equation 4x² + 10xy + 4y² = 36.Use rotation of coordinate axes through an appropriate acute angle $\theta$ to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( $\theta$ ) - v sin( $\theta$ ) , y = u sin( $\theta$ ) + v cos( $\theta$ ) . Then identify the conic section.

A) $A conic section is given by the equation 4x2 + 10xy + 4y2 = 36.Use rotation of coordinate axes through an appropriate acute angle \theta to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta ) - v sin( \theta ) , y = u sin( \theta ) + v cos( \theta ) . Then identify the conic section. A) + = 1, an ellipse B) + = 4, a circle C) - = 1, a hyperbola D) + = 1, an ellipse E) - = 1, a hyperbola$ + $A conic section is given by the equation 4x2 + 10xy + 4y2 = 36.Use rotation of coordinate axes through an appropriate acute angle \theta to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta ) - v sin( \theta ) , y = u sin( \theta ) + v cos( \theta ) . Then identify the conic section. A) + = 1, an ellipse B) + = 4, a circle C) - = 1, a hyperbola D) + = 1, an ellipse E) - = 1, a hyperbola$ = 1, an ellipse
B) $A conic section is given by the equation 4x2 + 10xy + 4y2 = 36.Use rotation of coordinate axes through an appropriate acute angle \theta to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta ) - v sin( \theta ) , y = u sin( \theta ) + v cos( \theta ) . Then identify the conic section. A) + = 1, an ellipse B) + = 4, a circle C) - = 1, a hyperbola D) + = 1, an ellipse E) - = 1, a hyperbola$ + $A conic section is given by the equation 4x2 + 10xy + 4y2 = 36.Use rotation of coordinate axes through an appropriate acute angle \theta to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta ) - v sin( \theta ) , y = u sin( \theta ) + v cos( \theta ) . Then identify the conic section. A) + = 1, an ellipse B) + = 4, a circle C) - = 1, a hyperbola D) + = 1, an ellipse E) - = 1, a hyperbola$ = 4, a circle
C) $A conic section is given by the equation 4x2 + 10xy + 4y2 = 36.Use rotation of coordinate axes through an appropriate acute angle \theta to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta ) - v sin( \theta ) , y = u sin( \theta ) + v cos( \theta ) . Then identify the conic section. A) + = 1, an ellipse B) + = 4, a circle C) - = 1, a hyperbola D) + = 1, an ellipse E) - = 1, a hyperbola$ - $A conic section is given by the equation 4x2 + 10xy + 4y2 = 36.Use rotation of coordinate axes through an appropriate acute angle \theta to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta ) - v sin( \theta ) , y = u sin( \theta ) + v cos( \theta ) . Then identify the conic section. A) + = 1, an ellipse B) + = 4, a circle C) - = 1, a hyperbola D) + = 1, an ellipse E) - = 1, a hyperbola$ = 1, a hyperbola
D) $A conic section is given by the equation 4x2 + 10xy + 4y2 = 36.Use rotation of coordinate axes through an appropriate acute angle \theta to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta ) - v sin( \theta ) , y = u sin( \theta ) + v cos( \theta ) . Then identify the conic section. A) + = 1, an ellipse B) + = 4, a circle C) - = 1, a hyperbola D) + = 1, an ellipse E) - = 1, a hyperbola$ + $A conic section is given by the equation 4x2 + 10xy + 4y2 = 36.Use rotation of coordinate axes through an appropriate acute angle \theta to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta ) - v sin( \theta ) , y = u sin( \theta ) + v cos( \theta ) . Then identify the conic section. A) + = 1, an ellipse B) + = 4, a circle C) - = 1, a hyperbola D) + = 1, an ellipse E) - = 1, a hyperbola$ = 1, an ellipse
E) $A conic section is given by the equation 4x2 + 10xy + 4y2 = 36.Use rotation of coordinate axes through an appropriate acute angle \theta to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta ) - v sin( \theta ) , y = u sin( \theta ) + v cos( \theta ) . Then identify the conic section. A) + = 1, an ellipse B) + = 4, a circle C) - = 1, a hyperbola D) + = 1, an ellipse E) - = 1, a hyperbola$ - $A conic section is given by the equation 4x2 + 10xy + 4y2 = 36.Use rotation of coordinate axes through an appropriate acute angle \theta to find the new equation of the conic section in the uv-coordinate axes , where x = u cos( \theta ) - v sin( \theta ) , y = u sin( \theta ) + v cos( \theta ) . Then identify the conic section. A) + = 1, an ellipse B) + = 4, a circle C) - = 1, a hyperbola D) + = 1, an ellipse E) - = 1, a hyperbola$ = 1, a hyperbola