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Write the equation in standard form for the circle with radius 22 centered at the origin.\newline______

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Q. Write the equation in standard form for the circle with radius 22 centered at the origin.\newline______
  1. Find standard form equation: We need to find the standard form equation of a circle with a given radius and center. 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 the radius.
  2. Identify center and radius: Since the circle is centered at the origin, the values of hh and kk are both 00. The radius rr is given as 22.
  3. Substitute values into equation: Substitute h=0h = 0, k=0k = 0, and r=2r = 2 into the standard form equation of a circle to get the equation for our specific circle.(x−0)2+(y−0)2=22(x - 0)^2 + (y - 0)^2 = 2^2
  4. Simplify the equation: Simplify the equation by squaring the radius and removing the unnecessary terms involving 00.x2+y2=4x^2 + y^2 = 4

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