Question

Write the standard form of the equation for the circle with the given center and radius.a. (0,-8); 8b. (-5,-10); √14

Answer 1

The standard form of the equation of a circle with center (h,k) and radius r is:

$(x-h)^2+(y-k)^2=r^2$

Substitute (h,k) = (0,-8) and r = 8 to find the first equation:

$\begin{gathered} (x-0)^2+(y-(-8))^2=8^2 \\ \Rightarrow \\ x^2+(y+8)^2=64 \end{gathered}$

Substitute (h,k) = (-5 , -10) and r = sqrt(14) to find the another equation.

$\begin{gathered} (x-(-5))^2+(y-(-10))^2=(\sqrt[]{14})^2 \\ \Rightarrow \\ (x+5)^2+(y+10)^2=14 \end{gathered}$