Question

The graph of the equation x ^ 2 + y ^ 2 - 16x + 6y + 14 = 0 is a circle. An equivalent form of this equation is (x - 8) ^ 2 + (y + 3) ^ 2 = M

What is the value of M?

Answer 1

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ghanami

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hello :

note :

an equation of the circle Center at the w(a,b) and ridus : r is :

(x-a)² +(y-b)² = r²

in this exercice : x²+y²-16x+6y+53=0

(x²-16x) +( y²+6y ) +53 = 0

(x² -2(8)x +8² - 8²) +(y² +2(3)x -3²+3² ) +53=0

(x² -2(8)x +8²) - 8² +(y² +2(3)x +3²)-3² +53=0

(x-8)² +( y+3)² = 20

the center is : w(8,-3) and ridus : r = √20

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Explanation: