Question

Let $C$ be a circle in the family of concentric circles $x^{2}+y^{2}=k^{2}$, where is a parameter. If $C$ passes through $(1,2)$, then the equation of $C$ is

• A. $x^{2}+y^{2}=5$
• B. $x^{2}+y^{2}=25$
• C. $x^{2}+y^{2}=\sqrt{5}$
• D. $x^{2}+y^{2}=4$
• E. $x^{2}+y^{2}=2$

Answer 1

Answer: (A)

Given equation of circle is $x^{2}+y^{2}=k^{2}$.
Since, it is passing through (1, 2).
$\therefore (1)^{2}+(2)^{2}=k^{2}$
$\Rightarrow 1+4=k^{2}$
$\Rightarrow k^{2}=5$
$\therefore $ Required equation of circle is $x^{2}+y^{2}=5$.