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Write the equation in standard form for the circle with radius 11 centered at the origin. _____

Write the equation in standard form for the circle with radius 1111 centered at the origin.\newline_____ \_\_\_\_\_

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Q. Write the equation in standard form for the circle with radius 1111 centered at the origin.\newline_____ \_\_\_\_\_
  1. Identify Center and Radius: We need to identify the center and the radius of the circle to write its equation in standard form. The standard form of a circle's equation is (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2, where (h,k)(h, k) is the center of the circle and rr is its radius.\newlineSince the circle is centered at the origin, we have:\newlineh=0h = 0\newlinek=0k = 0\newliner=11r = 11
  2. Substitute Values: Now we substitute the values of hh, kk, and rr into the standard form equation of a circle.(x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2Substituting h=0h = 0, k=0k = 0, and r=11r = 11, we get:(x−0)2+(y−0)2=112(x - 0)^2 + (y - 0)^2 = 11^2
  3. Simplify Equation: Simplify the equation by squaring the radius and removing the zeros since subtracting zero does not change the value.\newlinex2+y2=121x^2 + y^2 = 121\newlineThis is the equation of the circle in standard form.

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