Question

Find the equation of the circle with center at the origin and which passes through the point (3,4) ?

Answer 1

`x^2+y^2=25`

Explanation:

The radius passes from (0,0) to (3,4)
This means the radius is the hypotenuse of a right angle triangle with base 3 and height 4.

Using Pythagoras, `3^2+4^2=r^2`

`9+16=r^2`

`r^2=25`