Question

Give the equation of the circle centered at the origin and passing through the point (0,5)

Answer 1

Answer:

$x^{2} +y^{2}=25$

Step-by-step explanation

The standard equation of a circle centered at origin is  $x^{2} +y^{2} =r^{2}$

r = radius of the circle

The circle is passing through the point (0,5)

∴ radius  $r=\sqrt{(0-0)^{2}+(5-0)^{2} }$

               $r=\sqrt{0+25}$

               $r=\sqrt{25}$

               $r^{2}=25$

∴ The equation of the circle is

     $x^{2} +y^{2} = 25$