Hammond Stephens
09/17/2024 · Middle School
Deternine whether the equation represents a circle, parabola, ellipse, or hyperbola. Justify your answer by the three rules. \( -2 x^{2}+5 x-3 y^{2}+7 y=0 \) hyperbola) Rule 1: Rule \( 2: \) Rule \( 3: \) a. \( A=-2, B=0, C=-3 ; B^{2}-4 A C<0 ; 0^{2}-4(-2)(-3)<0 ;-24<0 \) b. \( x^{2} \) and \( y^{2} \) are multiplied by the different numbers with the different sign c. \( A C>0 ;-1(-3)>1 ; 3>1 \) d. \( x^{2} \) and \( y^{2} \) are multiplied by the different numbers with the same sign e. \( A=-1, B=2, C=-1 ; B^{2}-4 A C<0 ; 2^{2}-4(-1)(-1)<0 ;-16<0 \) f. circle g. parabola h. ellipse i. \( A C>0 ;-2(-3)>0 ; 6>0 \)
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The equation represents an ellipse.
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