Find the radius of the circle x^2 + y^2 +4x - 6y= 12
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to find the radius, we will write the equation in the standard form:
We know that:
(x+a)^2 + (y-a)^2 = r^2 where...
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x^2+y^2+4x-6y = 12.
To find the radius, we rwritte the equation as:
x^2 +4x +y^2 -6y = 12.
(x^2-4x+4^2) -4^2 + (y^2 -6x+3^2) -3^2 = 12
(x-4)^2 +(y-3)^2 = 12+4^2 +3^2
(x-4)^2 +(y-3)^2 = 37 = (sqrt37)^2.
This is a circle with centre (4 ,3) and radius sqrt37.
The equation that is given to us is : x^2 + y^2 +4x - 6y= 12
Now x^2 + y^2 +4x - 6y= 12
=> x^2 + 4x + 4+ y^2 + - 6y +9 = 12 +4+9
=> (x+2)^2 + (y-3)^2 = 25
Now the equation of a circle with center at (a,b) and radius r is given by
(x-a)^2 + (y-b)^2 = r^2
The equation we have (x+2)^2 + (y-3)^2 = 25 is the equation of a circle with the center at (-2 , 3) and the radius equal to 5.
Therefore the radius is 5.
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