Question

write the standard equation of the circle with center (-5, -9) and r = √7. the standard form of the equation of the circle is (type an equation. simplify your answer.)

Explanation:

Step1: Recall circle - equation formula

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

Step2: Substitute the given values

Here, \(h=-5\), \(k = - 9\), and \(r=\sqrt{7}\). Substituting these into the formula, we get \((x-(-5))^2+(y - (-9))^2=(\sqrt{7})^2\).

Step3: Simplify the equation

\((x + 5)^2+(y + 9)^2=7\)

Answer:

\((x + 5)^2+(y + 9)^2=7\)