This circle is centered at the point (4, 5), and the length of its radius is 3. What is the equation of the circle?A.(x + 4)2 + (y + 5)2 = 3B.(x - 5)2 + (y - 4)2 = 9C.(x - 4)2 + (y - 5)2 = 9D.(x2 - 4) + (y2 - 5) = 32SUBMITarrow_backPREVIOUS
Question
This circle is centered at the point (4, 5), and the length of its radius is 3. What is the equation of the circle?A.(x + 4)2 + (y + 5)2 = 3B.(x - 5)2 + (y - 4)2 = 9C.(x - 4)2 + (y - 5)2 = 9D.(x2 - 4) + (y2 - 5) = 32SUBMITarrow_backPREVIOUS
Solution
The equation of a circle in a coordinate plane is given by (x - h)² + (y - k)² = r², where (h, k) is the center of the circle and r is the radius.
Given that the circle is centered at the point (4, 5) and the length of its radius is 3, we can substitute these values into the equation.
So, h = 4, k = 5, and r = 3.
Substituting these values into the equation gives us (x - 4)² + (y - 5)² = 3².
Simplifying the right side of the equation gives us (x - 4)² + (y - 5)² = 9.
Therefore, the equation of the circle is (x - 4)² + (y - 5)² = 9.
So, the correct answer is C. (x - 4)² + (y - 5)² = 9.
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