Question

Give the equation of the circle centered at the origin and passing through the point , 0−9.

Answer 1

`x^2+y^2=81`

Explanation:

step 1

Find the radius of the circle

we know that

The radius of the circle is the distance between the center and any point on the circle

the formula to calculate the distance between two points is equal to

`d=\sqrt{(y2-y1)^(2)+(x2-x1)^(2)}`

we have the points

(0,0) and (0,-9)

substitute in the formula

`r=\sqrt{-9-0)^(2)+(0-0)^(2)}`

`r=\sqrt{-9)^(2)+(0)^(2)}`

`r=9/ units`

step 2

Find the equation of the circle

The equation of the circle in center radius form is equal to

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

we have

`(h,k)=(0,0)\\r=9\ units`

substitute

`(x-0)^2+(y-0)^2=9^2`

`x^2+y^2=81`