Question

If circle $S(x,y)=0$ touches the line $x+y-5=0$ at $(2,3)$ and $S(1,2)=-2.$ Then radius of circle is :-

• A. $\sqrt{2}$ units
• B. $4$ units
• C. $1/2$ units
• D. 0

Answer 1

Answer: (A)

$\sqrt{2}$ units

Given $S(1,2)=-2\cdots \left(1\right)⟹(1,2)$ is a inside point

Distance of $(1,2)$ from $(2,3)$ is $\sqrt{2}\cdots \left(2\right)$

Let Centre be $(a,b)⟹S(a,b)=-r^2\cdots \left(3\right)$

Distance between $(2,3)$ and $(a,b)$ will be $r\cdots \left(4\right)$

From $\left(1\right),\left(2\right),\left(3\right),\left(4\right)$

$r=\sqrt{2}$