Find the equation of the circle tangent to the x-axis at (6,0) and tangent to the y-axis

Question

anonymous · Answer

@amistre64 @phi

amistre64 · Answer

your thoughts?

anonymous · Answer

the tangent line goes through (6,0) but I'm not sure about the y axis part

amistre64 · Answer

well, we can always solve for k i spose ... unless you can determine a useful property of a circle and its tangents

anonymous · Answer

how do we solve for K... ?

amistre64 · Answer

(x-h)^2 + (y-k)^2 = r^2  is the equation of a circle centered at h,k right?

anonymous · Answer

so (6-h)^2+(0-k)^2=r^2 ?

amistre64 · Answer

that is one way to try an approach ...

amistre64 · Answer

|dw:1445298440396:dw|

amistre64 · Answer

tangent lines have normals that point to the center .

amistre64 · Answer

to the center of a circle tha tis

anonymous · Answer

ok

anonymous · Answer

ok how do we start this question ..im a bit confuse

amistre64 · Answer

depend on what you know .... my approach is not necessarily going to be your approach.

amistre64 · Answer

if we are tangent to the x axis, at 6,0 ... what does that limit our radius to if we also have to be tangent to the y axis?

anonymous · Answer

r=3?

amistre64 · Answer

not what im thinking ...

amistre64 · Answer

will our center be aong the x=6 axis?

anonymous · Answer

idk can it?

amistre64 · Answer

well, if normals to the tangents point to the center ... and we are tangent to the x axis at x=6,  |dw:1445299505006:dw|