Question

Find the equation of the circle,center on the y-axis, radius 2.5,and tangent to x-axis?

Answer 1

Equation of the circle is
`x^2+y^2-5y+18.75=0`

Explanation:

Center is `O-=(0,y)`
Tangent to x axis, means
with center`O-=(0,y)`
Radius is 2.5
Center is `)-=(0,2.5)`

Equation of circle is
`(x-0)^2+(y-2.5)^2=2.25^2`

`x^2+y^2-5y+25=6.25`

Simplifying

`x^2+y^2-5y+25-6.25=0`

`x^2+y^2-5y+18.75=0`

Answer 2

See a solution process below:

Explanation:

With the radius at 2.5, the center of the circle on the `y` axis and the `x` axis being a tangent, we then know the center of the circle is at: `(0, 2.5)`

The equation for a circle is:

`(x - color(red)(a))^2 + (y - color(red)(b))^2 = color(blue)(r)^2`

Where `(color(red)(a), color(red)(b))` is the center of the circle and `color(blue)(r)` is the radius of the circle.

Substituting the values we know from the problem gives:

`(x - color(red)(0))^2 + (y - color(red)(2.5))^2 = color(blue)(2.5)^2`

`x^2 + (y - color(red)(2.5))^2 = color(blue)(6.25)`