Question

For what value of $K$ will the line with equation $x=6$ be tangent to the circle with equation $x^2+y^2=K$?

• A. $6$
• B. $36$
• C. $72$
• D. $108$

Answer 1

The correct option is B $36$

We substitute $x=6$ in the equation of circle $x^2+y^2=K$ as follows:

$x^2+y^2=K$

$\Rightarrow (6{)}^2+y^2=K$

$\Rightarrow 36+y^2=K$

$\Rightarrow y^2=K-36$

Since for a tangent point, there can only be one value for $y$, this means that $K-36$ has to be $0$ that is:

$K-36=0$

$\Rightarrow K=36$

Hence, $K=36$