# How do you find an equation of the circle of radius 4 that is tangent to the x-axis and has its center on x-2y=2?

Mar 19, 2016

The given circle touches x-axis and its radius is 4 ,so its center will be 4 unit distance apart from the point of contact on x- axis i.e. the ordinate of its center should be +4 or-4. Let the x-coordinate of its center be h then its center would be (h,4) OR (h,-4)

Again it is given that the center is on the line $x - 2 y = 2$
So we can write for center (h,4)
$h - 2 \cdot 4 = 2 \implies h = 10$
equation of the circle having center$\left(10 , 4\right)$and radius 4
${\left(x - 10\right)}^{2} + {\left(y - 4\right)}^{2} = 16$

for center (h,-4)
$h - 2 \cdot \left(- 4\right) = 2 \implies h = - 6$

equation of the circle having center$\left(- 6 - 4\right)$and radius 4
${\left(x + 6\right)}^{2} + {\left(y + 4\right)}^{2} = 16$