Question

Exercises to Chapter 1 33 1.9 In (1.12) there is a list of possible ways in which two conics can intersect. Write down equations showing that each possibility really occurs. Find all the singular conics in the corresponding pencils. (Hint: you will save yourself a lot of trouble by using symmetry and a well chosen coordinate system. Hint for 1.2: it is known from elementary number theory that -1 is a quadratic residue modulo p if and only if p = 2 or p = 1 mod 4.

Answer 1

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