Question

Find the equation of the circles which touches the x -axis at a distance of 3 from the origin and center at $(0,4)$

Answer 1

Center of circle $(0,4)$

The point it passes through $(\pm 3,0)$

So radius is given as distance between them

$r=\sqrt{(3-0{)}^2+(0-4{)}^2}r=\sqrt{9+16}=5$

So the equation of circle is $x^2+(y-4{)}^2=2$