First slide

Definition of a circle

Question

The equations of the circles which touch both the
axes and the line $x = a$ are

Moderate

A

$x^{2} + y^{2} \pm a x \pm a y + \frac{a^{2}}{4} = 0$
B

$x^{2} + y^{2} + a x \pm a y + \frac{a^{2}}{4} = 0$
C

$x^{2} + y^{2} - a x \pm a y + \frac{a^{2}}{4} = 0$
D

none of these

Solution

Since the circle touches both the axes and the line
$x = a .$ Therefore, coordinates of its centre are $(a / 2, \pm a / 2)$ and
radius $a / 2 .$
Hence, the required circles are
${(x - \frac{a}{2})}^{2} + {(y \mp \frac{a}{2})}^{2} = {(\frac{a}{2})}^{2} \Rightarrow x^{2} + y^{2} - a x \pm a y + \frac{a^{2}}{4} = 0$

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