Question

Writing a equation of a circle centers at the origin

Answer 1

`x^2+y^2=100`

Step-by-step explanation

The general equation of a circle is:

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

where (h, k) = the center of the circle

r = radius of the circle (i.e. distance from any point on its circumference to the center of the circle)

The center of the circle is the origin, that is:

`(h,k)=(0,0)`

To find the radius, apply the formula for distance between two points:

`r=\sqrt[]{(x_1-h)^2+(y_1-k)^2_{}}`

where (x1, y1) is the point the circle passes through

Hence, the radius is:

`\begin{gathered} r=\sqrt[]{(0-0)^2+(-10-0)^2}=\sqrt[]{0+(-10)^2} \\ r=\sqrt[]{100} \\ r=10 \end{gathered}`

Hence, the equation of the circle is:

`\begin{gathered} (x-0)^2+(y-0)^2=(10)^2 \\ \Rightarrow x^2+y^2=100 \end{gathered}`