Question

Write the equation of each circle given its center and a point P that it passes through

Answer 1

x²+y² = 4 is the equation of given circle.

Explanation:

We have given the center (0,0) and a point P (2,0) from which the circle is passes.

So, the radius of the circle is :

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

r= 2

The equation of circle is :

(x - x₁)² +(y - y₁)² = r² where (x₁,y₁) is the center of circle.

Putting the value in above equation we get,

(x-0)²+(y-0)² = (2)²

x²+y² = 4 is the equation of given circle.

Answer 2

`{x}^(2) + {y}^(2) = 4`

EXPLANATION

The circle passes through P=(2,0) and centered at (0,0).

The radius of this circle is

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

The equation is given by:

`{x}^(2) + {y}^(2) = {r}^(2)`

This implies that

`{x}^(2) + {y}^(2) = {2}^(2)`

`{x}^(2) + {y}^(2) = 4`