Question from http://www.sgforums.com/forums/2297/topics/345695
Find the range of values of p for which the line y - x = 2 meets the curve y² + (x+p)² = 2
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Answer:
y = 2 + x -----------------------(1)
y² + (x+p)² = 2 -----------------(2)
Sub (1) into (2)
2x² + (4 + 2p) x + (2 + p²) = 0
Discriminant ≥ 0
i.e. b² - 4ac ≥ 0
16 +16p + 4p² - 16 - 8p² ≥ 0
16p - 4p² ≥ 0
4p (4 - p) ≥ 0
Draw a n-shape curve with roots 0 and 4 and shade the above since coefficient of p² ≥ 0
Thus,
0 ≤ p ≤ 4
