Question

Write an equation of a circle that has the center at the origin and goes through (-3,-6)

Answer 1

`x^(2) +y^(2) = 45`

Explanation:

General Equation of circle is

`(x-x_1)^(2) +(y-y_1)^(2) = r^(2)`----------- (1)

Here

`(x_1, y_1)= (0, 0)`

Radius r is distance from origin (x1, y1) to point (x2, y2)=(-3, -6)

`r=\sqrt{(x_2-x_1)^(2) + (y_2-y_1)^(2) }`

`r= \sqrt{(-3-0)^(2) + (-6-0)^(2) }`

`r= √(9+36)`

`r=√(45)`

Substituting values in equation (1)

`(x-0)^(2) +(y-0)^(2) =( √(45))^(2)`

`x^(2) +y^(2) = 45`