# Find the equation of a circle with

Question:

Find the equation of a circle with Centre $(a, a)$ and radius $\sqrt{2}$

Solution:

The general form of the equation of a circle is:

$(x-h)^{2}+(y-k)^{2}=r^{2}$

Where, $(\mathrm{h}, \mathrm{k})$ is the centre of the circle.

$r$ is the radius of the circle.

Substituting the centre and radius of the circle in he general form:

$\Rightarrow(x-a)^{2}+(y-a)^{2}=(\sqrt{2})^{2}$

$\Rightarrow(x-a)^{2}+(y-a)^{2}=2$

Ans; equation of a circle with Centre $(a, a)$ and radius $\sqrt{2}$

is:

$(x-a)^{2}+(y-a)^{2}=2$