What is the equation of a circle with center \((2, -5)\) and radius \(4\)?

( x − h ) 2 + ( y − k ) 2 = r 2 ( x − 2 ) 2 + ( y + 5 ) 2 = 16

Answered by konrad509 | 2024-06-10

[Equation\ of\ circle\\ r^2=(x-a)^2+(y-b)^2\\ a,b- \ coordinates\ of\ center\ of\ circle\\ (a,b)=(2,-5) \\ r-\ radius\\ r=4\\Solution:\ 4^2=(x-2)^2+(y+5)^2\\\
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Answered by luana | 2024-06-10

The equation of the circle with center (2, -5) and radius 4 is given by (x - 2)^2 + (y + 5)^2 = 16. This follows the standard form of the circle's equation where (h, k) represents the center and r is the radius. By substituting the values for the center and calculating the square of the radius, we arrive at the final equation.
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Answered by konrad509 | 2025-02-10