In the equation x2+(yk)2=16, for what values of K is this circle tangent to y = 3?

1 Answer
Jul 16, 2016

x2+(y+1)2=16

or

x2+(y7)2=16

Explanation:

Standard form for the equation of a circle is

(xa)2+(yb)2=r2

From this we can see that r2=16r=4

y=3, horizontal line across at this level so we need the top (or bottom) of the circle to be at y=3. The radius is 4 so we want the centre of the circle to be 4 below y=3, ie y=1 or 4 above y=3, ie y=7

Therefore k=1 or k=7