Questions: Write the standard form of the equation and the general form of the equation of the circle with radius r and center (n, x). Then graph the circle r=2; (x)=(-2,0) The standard form of the equation of this circle is (x-2)^2+(y+2)^2

Solution Steps

The circle has a radius \( r = 2 \) and a center at \( (-2, 0) \).

The standard form of the equation of a circle with center \((h, k)\) and radius \(r\) is: \[ (x - h)^2 + (y - k)^2 = r^2 \] Substituting the given values, \( h = -2 \), \( k = 0 \), and \( r = 2 \), we get: \[ (x + 2)^2 + (y - 0)^2 = 2^2 \] \[ (x + 2)^2 + y^2 = 4 \]

The general form of the equation of a circle is: \[ x^2 + y^2 + Dx + Ey + F = 0 \] Expanding the standard form: \[ (x + 2)^2 + y^2 = 4 \] \[ x^2 + 4x + 4 + y^2 = 4 \] Subtract 4 from both sides: \[ x^2 + y^2 + 4x = 0 \] Thus, the general form is: \[ x^2 + y^2 + 4x = 0 \]

Final Answer