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Let m and n be an integer and m > n. You can generate triples with: a = 2mn b = m^2 - n^2 c = m^2 + n^2 For example, let m = 4 and n = 3. a = 2(3)(4) = 24 b = 4^2 - 3^2 = 7 c = 4^2 + 3^2 = 25 Therefore, you'd have the triple (24, 7, 25). Check: 24^2 + 7^2 = 25^2 ==> 576 + 49 = 625 ==> 625...

-y^2 - 4x + 4y - 4 = 0 ==> y^2 + 4x - 4y + 4 = 0 This appears to be a parabola with a vertical directix. y^2 + 4x - 4y + 4 = 0 ==> y^2 - 4y + 4 = -4x ==> (y - 2)^2 = -4x ==> (-1/4)(y - 2)^2 + 0 = x Comparing the leading coefficent in-front of the squared binomial, we see that p = -1. The...