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  3. 12 let c be the conic given by the equation...

Question: 12 let c be the conic given by the equation...

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1.2. Let C be the conic given by the equation and let 6 be the determinant 2a b d (a) Show that if 0, then C has no singular points, ie., show that there are no points (x, y) satisfying OF (b) Conversely, show that if 0 and b2-4ac 0, then there is a unique singular (c) Let L be the line y = αx + β with αメ0. Show that the intersection of L (d) Determine the conditions on the coefficients which ensure that the intersection point on C and C consists of either zero, one, or two points. LnC consists of exactly one point. What is the geometric significance of these conditions. (Note that there will be more than one case to consider.)

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