# construct an equationi have an assignment and i've to construct equation of a circle with radius 6 and center C(2,-4)

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The standard form of the equation of a circle with center (a, b) and radius r is (x - a)^2 + (y - b)^2 = r^2

Here the center is (2 , -4) and the radius is 6, so we have

(x - 2)^2 + (y + 4)^2 = 36

=> x^2 + 4 - 4x + y^2 + 16 + 8y = 36

=> x^2 + y^2 - 4x + 8y - 16 = 0

**The required equation of the circle is x^2 + y^2 - 4x + 8y - 16 = 0**

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We'll recall the standard form of theÂ equation of the circle:

(x - h)^2 + (y - k)^2 = r^2

h and k represent the coordinates of the center of the circle and r is the value of the radius of the circle.** **

Now, we can write the equation of the circle in the standard form:

(x - 2)^2 + (y + 4)^2 = 36

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