Answer to Question #87454 in Analytic Geometry for Jjww

Question

Write an equation for the circle with centre (0,0) if the point A(6,2) lies on the circle

Answer 1

The general equation of a circle can be written in the form as follows:

$$(x-x_0)^2 + (y-y_0)^2 = r^2,$$

where (x₀,y₀) is the position of the centre of the circle, r is its radius. As long as the centre is located at (0,0), the radius (here we need this value squared) of the circle can be calculated as the distance between its centre and point A(6,2) belonging to it:

$$r^2 = 6^2 + 2^2 = 40$$

Finally, we obtain:

$$x^2 + y^2 = 40,$$

which is the answer on the question