The general form of the equation of a circle is  x2  +  y2  + 42x  + 38y  − 47 = 0. the equation of this circle in standard form is . the center of the circle is at the point , and its radius is units. the general form of the equation of a circle that has the same radius as the above circle is . nextreset

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

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
Solution:
-2h = 42
   h = 21

-2k = 38
   k = 19

-47 = h^2 + k^2 - r^2
-47 = 21^2 + 19^2 - r^2
r^2 = 849
    r = √849

Answers:
1.) Standard form : (x+21)² + (y+19)² = 849
2.) Center of the circle : (h,k) = (21,19)
3.) Radius of the circle : r = √849
4.) Equation of a circle that has the same radius as the above circle is : x^2 + y^2 - 50x - 30y + 1 = 0

You can solve the last one through trial and error. Its h - 25; k - 15.
1 = h^2 + k^2 - r^2
1 = -25^2 + -15^2 - r^2
r^2 = 849
    r = √849  :  which has the same radius as the given equation.

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