The Standard form of the equation of circle is (x+21)² + (y+19)² = 849
To transform general form to a standard form, you can use completing the square method or you can convert this equation
x² + y² + Dx + Ey + F = 0 to x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0
Here, Given: x² + y² + 42x + 38y − 47 = 0
Required: Find the values of h, k, and r using this formula
x² + y² + (-2h)x + (-2k)y + (h²+k²-r²) = 0
On comparing we get,
-2h = 42
h = 21
-2k = 38
k = 19
-47 = h² + k² - r²
-47 = 21² + 19² - r²
r² = 849
r = √849
Thus, the Standard form of the equation of circle is (x+21)² + (y+19)² = 849
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