find the center-radious form of the equation of the circle with center = (2,-6) and the tangent to the y-axis.

Question

college algebra

Answer 1

Find the center-radious form of the equation of the circle with center = (2,-6) and the tangent to the y-axis.

If tangent to the y - axis then the point (0, -6) is the point of contact (as tangent to circle _|_ radius at point of contact)

Therefore radius = 2

Therefore required circle is

(x - 2)² + (y + 6)² = 2²

Answer 2

The general equation of a circle at some point (a,b) is
(x-a)^2 + (y-b)^2 = r^2 where r is the radius.
If the circle is tangent to the y-axis, then the radius must be the distance to the y-axis from the x point of center ie r=2. If you draw it out in a cursory fashion you will see this easily.
TIP: always draw these things out, it makes it so much easier
Now you are given that a=2 and b=-6, so the equation is
(x-2)^2+(y--6)^2=2^2, or
(x-2)^2+(y+6)^2=4

Answer 3

(x-2)^2 + (y+6)^2 = 4