Question

Rewrite x^2+y^2+6x-4y-3=0 in standard form

Answer 1

(x +3)^2 +(y -2)^2 = 16

Explanation:

Complete the squares.

(x^2 +6x) +(y^2 -4y) -3 = 0

(x^2 +6x +9) +(y^2 -4x +4) = 16 . . . . add 9+4+3 = 16

(x +3)^2 +(y -2)^2 = 16

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Additional comment

The square (x +a)^2 is (x^2 +2ax + a^2). When you have (x^2 +2ax), you complete the square by adding the square of half the x-coefficient.