Question

The equation of the circle which touches both the axis and whose radius is $a$, is:

• A. $x^2+y^2-2ax-2ay+a^2=0$
• B. $x^2+y^2+ax-ay-a^2=0$
• C. $x^2+y^2+2ax+2ay-a^2=0$
• D. $x^2+y^2-ax-ay+a^2=0$

Answer 1

The correct option is A

$x^2+y^2-2ax-2ay+a^2=0$

Explanation for the correct option:

Finding the equation of circle,

Given the radius of the circle is $a$ and the circle touches both the axis.

Visualizing the given information:

We see that the coordinates of the centre will be $(a,a)$

We know that the equation of the circle is

$x^2+y^2+2gx+2fy+c=0$

Therefore, the equation of the circle will be

$$\begin{gathered} {(x-a)}^2+{(y-a)}^2=a^2 \\ {x}^2+y^2-2ax-2ay+a^2=0 \end{gathered}$$

Hence, the correct answer is Option (A).