Question

write the standard form of the equation of the circle with the given center and radius. center (2, -4), r = 7 type the standard form of the equation of the circle. (simplify your answer.)

Explanation:

Step1: Recall the standard form of a circle's equation

The standard form of the equation of a circle is \((x - h)^2+(y - k)^2=r^2\), where \((h,k)\) is the center and \(r\) is the radius.

Step2: Substitute the given values

Given \(h = 2\), \(k=-4\), and \(r = 7\). Substitute into the formula: \((x - 2)^2+(y-(-4))^2=7^2\).

Step3: Simplify the equation

Simplify \((y - (-4))\) to \((y + 4)\) and \(7^2\) to \(49\). So the equation becomes \((x - 2)^2+(y + 4)^2=49\).

Answer:

\((x - 2)^2+(y + 4)^2=49\)