In the equation x^{2}+(y-k)^{2}=16, for what values of K is

esbagoar7kh

esbagoar7kh

Answered question

2022-04-24

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

Answer & Explanation

vanvanvan4ie

vanvanvan4ie

Beginner2022-04-25Added 12 answers

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

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