Question

For what value of $K$ is the point $(K,2K)$ outside the circle with equation $x^2+y^2=5$?

• A. $|K|=0$
• B. $|K|>1$
• C. $|K|>2$
• D. $|K|>\frac{1}{2}$

Answer 1

The correct option is B $|K|>1$

Since the point $(K,2K)$ is outside the circle with equation $x^2+y^2=5$,

Therefore, substitute $x=K$ and $y=2K$ in the equation $x^2+y^2=5$ as shown below:

$(K{)}^2+(2K{)}^2=5$

$\Rightarrow K^2+4K^2>5$

$\Rightarrow 5K^2>5$

$\Rightarrow K^2>1$

$\Rightarrow |K|>1$