Question

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?

Answer 1

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-2y=2`
So we can write for center (h,4)
`h-2*4=2 => h=10`
equation of the circle having center`(10,4)`and radius 4
`(x-10)^2+(y-4)^2=16`

for center (h,-4)
`h-2*(-4)=2=>h=-6`

equation of the circle having center`(-6-4)`and radius 4
`(x+6)^2+(y+4)^2=16`