Answer:
r = 2
equation of the circle: [tex](x-2)^2+(y+5)^2=4[/tex]
Step-by-step explanation:
a) given the center of the circle as (2,-5).
we can say that
it is also given that the circle is tangent to the x-axis, this means that the circle touches the x-axis.
And we already know how far away the circle's center is from the x-axis, i.e. 2 units. Hence this is the radius.
r = 2.
b) Given the center of the circle we can its equation using the formula
[tex](x-a)^2+(y-b)^2=r^2[/tex]
where, (a,b) are the coordinates of the center of the circle. and r is the radius
hence (a,b) = (2,-5) and r = 2
[tex](x-2)^2+(y-(-5))^2=(2)^2[/tex]
[tex](x-2)^2+(y+5)^2=4[/tex]
this is the equation of the circle!
