Question

How do you find the equation of a circle center at the origin; passes through (10, 10)?

Answer 1

`x^2+y^2=10sqrt(2)`

Explanation:

You can use Pythagoras for this by treating the x-axis and y-axis as if they were sides of a triangle and a line from the origin to the point `(10,10)` as though it is the hypotenuse.

Let the hypotenuse be the radius (r) of the circle

Then `r^2=x^2+y^2`

`=>r=sqrt(10^2+10^2) = sqrt(200)`

`=>r=sqrt(2xx10^2)=10sqrt(2)`

So the equation of the circle is:

`x^2+y^2=10sqrt(2)`