Question

What is the equation of a circle, centred on the origin, which passes through the point `(8,3)`?

Answer 1

In this case the equation is `x^2+y^2=73`

Explanation:

All points on a circle are equidistant (the same distance) from the centre.

We can find the radius of the circle: `r=sqrt(x^2+y^2)=sqrt(8^2+3^2)=sqrt(73)` units.

The equation of a circle with its centre at the origin is is `x^2+y^2=r^2`

In this case:

`x^2+y^2=73`