Question

How do you write the standard equation of the circle the given center that passes with through the given point: center (0, 0); point (3, 4)?

Answer 1

`x^2+y^2=25`

Explanation:

`"the equation of a circle in standard form is"`

`•color(white)(x)(x-a)^2+(y-b)^2=r^2`

`"where "(a,b)" are the coordinates of the centre and r is"`
`"the radius"`

`"here "(a,b)=(0,0)`

`(x-0)^2+(y-0)^2=r^2`

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

`"the radius is the distance from the centre to the given "`
`"point the circle passes through"`

`r=sqrt(3^2+4^2)=sqrt25=5`

`x^2+y^2=25larrcolor(red)"equation in standard form"`