Question

write the standard form of the equation of the circle with the given center and radius c(6,-9);√14

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: Identify the values of \(h\), \(k\), and \(r\)

Given the center \(C(6,-9)\), so \(h = 6\), \(k=-9\), and radius \(r = \sqrt{14}\).

Step3: Substitute the values into the standard form

Substitute \(h = 6\), \(k=-9\), and \(r=\sqrt{14}\) into \((x - h)^2+(y - k)^2=r^2\).
We get \((x - 6)^2+(y+9)^2=(\sqrt{14})^2\).

Answer:

\((x - 6)^2+(y + 9)^2=14\)