Question

Find the equation of a circle with the center at ( 0, 0 ) and a radius of 1.

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given details

`\begin{gathered} center:(0,0) \\ radius:1 \end{gathered}`

STEP 2: Write the formula for equation of a circle

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

STEP 3: Find the equation of the circle

`\begin{gathered} By\text{ substitution,} \\ (x-0)^2+(y-0)^2=1^2 \\ x^2+y^2=1^2 \\ x^2+y^2=1 \end{gathered}`

Hence, the equation of the circle is given as:

`x^2+y^2=1^`