# Equation of tangent of circle whose centre is (0,0) at a point (2,2) which lie on circle?

$\begin{array}{1 1}(a)\;x+y=2\\(b)\;x+y=4\\(c)\;x^2+y^2=4\\(d)\;x+y=3\end{array}$

Radius =$\sqrt{(2)^2+(2)^2}=2\sqrt 2$
Slope of tangent $=m_1\times m_2=-1$
$m_1$-Slope of line formed by (2,2) and (0,0)
$m_2$-Slope of tangent
$\large\frac{2}{2}$$\times m_2=-1$
$m_2=-1$
Equation of tangent $(y-2)=-1(x-2)$
$(x+y)=4$
Hence (b) is the correct answer.