Question

Write the equation in standard form for the circle passing through (12,0) centered at the origin

Answer 1

From the question, we are told that the circle pass through (12, 0) and centered at origin. So this means to find the radius, the diagram below would be helpful

From the diagram above, we have that

`\begin{gathered} r^2=x^2+y^2 \\ r^2=12^2+0^2 \\ r^2=144 \\ r=√(144) \\ r=12 \end{gathered}`

Equation of a circle is given as

`\begin{gathered} (x-h)^2+(y-k)^2=r^2 \\ We\text{ are told that the center is at the origin, so} \\ (h,k)=(0,0) \\ equation\text{ becomes } \\ (x-0)^2+(y-0)^2=12^2 \\ x^2+y^2=12^2 \end{gathered}`

Hence the answer is

`x^2+y^2=12^2`