First slide

Definition of a circle

Question

Equation of a circle which passes through (3, 6) and touches the axes, is

Moderate

A

$x^{2} + y^{2} + 6 x + 6 y + 3 = 0$
B

$x^{2} + y^{2} - 6 x - 6 y - 9 = 0$
C

$x^{2} + y^{2} - 6 x - 6 y + 9 = 0$
D

none of these

Solution

The equation of a circle touching the co-ordinate
axes is
$(x - a)^{2} + (y - a)^{2} = a^{2}$ or, $x^{2} + y^{2} - 2 a x - 2 a y + a^{2} = 0$
This passes through (3, 6).
$∴ 9 + 36 - 6 a - 12 a + a^{2} = 0 \Rightarrow a = 3, 15 .$
Hence, the required circle are
$x^{2} + y^{2} - 6 x - 6 y + 9 = 0$ or, $x^{2} + y^{2} - 30 x - 30 y + 225 = 0 .$

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