Determine the equation of the circle with center left bracket, minus, 2, comma, minus, 3, right bracket(−2,−3) containing the point left bracket, 4, comma, 5, right bracket(4,5).
Question
Determine the equation of the circle with center left bracket, minus, 2, comma, minus, 3, right bracket(−2,−3) containing the point left bracket, 4, comma, 5, right bracket(4,5).
Solution
The equation of a circle is given by the formula (x-h)² + (y-k)² = r², where (h,k) is the center of the circle and r is the radius.
Given the center of the circle is (-2,-3), we can substitute h = -2 and k = -3 into the equation, giving us:
(x - (-2))² + (y - (-3))² = r² => (x + 2)² + (y + 3)² = r²
We also know that the circle contains the point (4,5). We can substitute x = 4 and y = 5 into the equation to solve for r²:
(4 + 2)² + (5 + 3)² = r² => 6² + 8² = r² => 36 + 64 = r² => 100 = r²
So, the equation of the circle is (x + 2)² + (y + 3)² = 100.
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