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

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

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

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

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None of these

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Solution

The correct option is B $x^{2} + y^{2} - 6 x - 6 y + 9 = 0$
Equation of circle touching both the axis and having radius $R$ is given by,
$(x - r)^{2} + (y - r)^{2} = r^{2}$
Also it passes through (3,6)
$\Rightarrow (3 - r)^{2} + (6 - r)^{2} = r^{2}$
$\Rightarrow r^{2} - 18 r + 45 = 0$
$\Rightarrow r = 15, 3$
Hence required circle is,
$x^{2} + y^{2} - 6 x - 6 y + 9 = 0$ or $x^{2} + y^{2} - 30 x - 30 y + 225 = 0$

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Q. Equation of a circle which passes through (3, 6) and touches the axes is
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(d) None of these

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

The correct option is B x2+y2−6x−6y+9=0Equation of circle touching both the axis and having radius R is given by,(x−r)2+(y−r)2=r2Also it passes through (3,6)⇒(3−r)2+(6−r)2=r2⇒r2−18r+45=0 ⇒r=15,3Hence required circle is,x2+y2−6x−6y+9=0 or x2+y2−30x−30y+225=0

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