Question

What is the standard equation of a circle with center (0, -5) and radius 7?

Answer 1

Given:

`\begin{gathered} center(0,-5) \\ radius=7 \end{gathered}`

The standard equation of a circle is given by;

`\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ \\ where; \\ (h,k)\text{ is the center of the circle} \\ r\text{ is the radius} \end{gathered}`

Hence,

`\begin{gathered} h=0 \\ k=-5 \\ r=7 \end{gathered}`

Substituting these values into the formula, the equation of the circle is;

`\begin{gathered} (x-0)^2+(y-(-5))^2=7^2 \\ x^2+(y+5)^2=49 \end{gathered}`

Therefore, the equation of the circle with center (0,-5) and radius 7 is;

`x^2+(y+5)^2=49`