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Determine whether the following statement makes sense or does not make sense and explain your reasoning. It is noticed that depending on the values for
Determine whether the following statement makes sense or does not make sense and explain your reasoning. It is noticed that depending on the values for A and C, assuming that they are not both zero, the graph of Ax" + Cy + Dx + Ey + F =0 can represent any of the conic sections. Choose the correct answer below. A. The statement makes sense. If the values of A and C are equal, the equation can be divided by A, making the coefficients of the x and y"-terms 1. So, this equation represents a circle. If one of A or C is zero, then AC = 0, which eliminates either of the x and y -terms. So, this equation represents a parabola. If A # C and AC 0, this means A and C, and alternatively x" and y"-terms have the same sign. So, this equation represents an ellipse. O B. The statement makes sense. If the values of A and C are equal, the equation represents a circle. If the values of A and C are not equal, the equation represents an ellipse. If one of A or C is zero, the equation represents a parabola. The statement does not make sense because the type of the conic section represented by the equation Ax" + Cy" + Dx + Ey + F =0 depends on the values of D, E, and F, and not A and C. D. The statement does not make sense because regardless of the values of A and C, the equation Ax" + Cy + Dx + Ey + F =0 does not represent any conic
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