Question

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

Answer 1

(x-1)²+(y-1)² = 37 is the equation of circle.

Explanation:

We have given the center (1,1) and a point P (2,-5) from which the circle is passes.

So, the radius of the circle is :

r=
`\sqrt{(2-1)^(2)+(1-(-5))^(2)}`

r =
`√(37)`

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-1)²+(y-1)² = (√37)²

(x-1)²+(y-1)² = 37 is the equation of circle.

Answer 2

`(x-1)^2+(y-1)^2=37.`

Explanation:

If the center of the circle is (1,1) and the circle passes through the point (2,-5), then the radius of the circle is

`r=√((1-2)^2+(1-(-5))^2)=√(1+36)=√(37).`

The equation of the circle with center
`(x_0,y_0)` and radius r is

`(x-x_0)^2+(y-y_0)^2=r^2.`

In your case, the equation is

`(x-1)^2+(y-1)^2=37.`