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A cruve is respresented by C=21x^(2)-6xy+29y^(2)+6x-58y-151=0 The center of the conic C is |
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Answer» (1,0) `2(x-3y+3)^(2)+2(3x+y-1)^(2)=180` or `((x-3y+3)^(2))/(60)+((3x+y-1)^(2))/(90)=1` or `((x-3y+3)/(sqrt(1+3^(2))sqrt(6)))^(2)+((3x+y-1)/(3sqrt(1+3^(2))))=1` Thus, C is an ellipse whose lengths of axes are `6,2sqrt(6)`. The minor and the major axes are `x-3y+3=0 and 3x+y-1=0`, respectively. Their POINT of INTERSECTION gives the center of the center of the conic. THEREFORE, Center `-=(o,1)` |
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