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x2 + 10x + y2 + 20y - 19 = 0

x2 + 10x + y2 + 20y = 19

Complete the squares on the LHS:

x2 + 10x + 25 + y2 + 20y + 100 = 19 + 25 + 100 = 144

Simplify LHS:

(x + 5)2 + (y + 10)2 = 122

This is the equation of all points whose distance form the point (-5, -10) is 12 units. That is, the circle with centre (-5, -10) and radius = 12 units.

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13y ago

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