Question

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

Answer 1

`x^(2) +y^(2)=25`

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=√(0+25)`

`r=√(25)`

`r^(2)=25`

∴ The equation of the circle is

`x^(2) +y^(2) = 25`