The equation of the circle having a center located at (-2,2) and the circumference of circle 16(pie) is,
[tex](x+2)^2+(y-2)^2=64[/tex]
What is the equation of circle?
The equation of the circle is the equation which is used to represent the circle in the algebraic equation form with the value of center point in the coordinate plane and measure of radius.
The standard form of the equation of the circle can be given as,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Here (h,k) is the center point of the circle and (r) is the radius of the circle.
The center point of the circle is (-2, 2) and the circumference of the circle is 16π.
Let the radius of the circle is r. As the circumference of the circle is twice the product of its radius and pi.
Thus,
[tex]16\pi=2\pi r\\r=\dfrac{16\pi}{2\pi}\\r=8[/tex]
Thus the radius of the circle is 8 units.
Put the values in the above equation of circle as,
[tex](x-(-2))^2+(y-2)^2=(8)^2\\(x+2)^2+(y-2)^2=(8)^2\\(x+2)^2+(y-2)^2=64[/tex]
Thus, the equation of the circle having a center located at (-2,2) and the circumference of circle 16(pie) is,
[tex](x+2)^2+(y-2)^2=64[/tex]
[tex](x+2)^2+(y-2)^2=64[/tex]
Learn more about the equation of circle here;
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