Answer:
the equation of circle is x² + y² + 6x - 24y + 128 = 0
Step-by-step explanation:
To find the general form of the equation of the circle with center A (-3, 12) and radius r=5, we simply use this formula;
General Equation of a circle is (x - a)² + (y-b)² = r²
(a,b) are the two point at the center of the circle which are (-3, 12)
which implies a = -3 and b = 12
r is the radius of the circle which is given as 5 from the above diagram
to get r², we simply square 5 and so r² = 25
We can now plug in the values of our variables into the equation
(x - a)² + (y-b)² = r²
(x - [-3])² + ( y - 12)² = 5²
(x +3)² + ( y - 12)² = 5²
we will expand all the brackets
x² + 6x + 9 + y² -24y + 144 = 25
x² +6x + y² -24y + 153 = 25
Take 25 to the left hand side of the equation
x² +6x + y² -24y + 153 - 25 = 0
x² +6x + y² -24y + 128 = 0
Rearranging the equation to give us a standard form of the equation of the circle, we have;
x² + y² + 6x - 24y + 128 =0
{Note: (x + 3)² = (x+3)(x+3) = x² + 6x + 9 and
(y - 12)² = (y -12)(y-12) = y² - 24y + 144}
Therefore the general form of the equation of a circle with center(-3, 12) and radius 5 is x² + y² + 6x - 24y + 128 =0
