The centre of the circle passing through  (0, 0) and (1, 0) and touching the circle x^{2}+y^{2}=9   is

  • Option 1)

    \left ( \frac{1}{2},\frac{1}{2} \right )\;

  • Option 2)

    \; \left ( \frac{1}{2},-\sqrt{2} \right )\;

  • Option 3)

    \; \left ( \frac{3}{2},\frac{1}{2} \right )\;

  • Option 4)

    \; \left ( \frac{1}{2},\frac{3}{2} \right )\;

 

Answers (1)
V Vakul

As we learnt in

Common tangents of two circles -

When two circles touch each other internally, there is only one common tangent.

- wherein

 

 OA =OB \\ \sqrt{h^{2}+k^{2}} =\sqrt{(h -1)^{2}+k^{2}}

2h-1 =0

h =\frac{1}{2}

Also \sqrt{h^{2}+k^{2}}=\frac{3}{2}

\left(\frac{1}{2} \right )^{2}+k^{2}=\left(\frac{3}{2} \right )^{2}

k^{2}=\frac{9}{4}-\frac{1}{4}=2

k=\pm \sqrt{2}

Point P is \left ( \frac{1}{2},+\sqrt{2} \right ) or \left (\frac{1}{2},-\sqrt{2} \right )

 


Option 1)

\left ( \frac{1}{2},\frac{1}{2} \right )\;

This option is incorrect.

Option 2)

\; \left ( \frac{1}{2},-\sqrt{2} \right )\;

This option is correct.

Option 3)

\; \left ( \frac{3}{2},\frac{1}{2} \right )\;

This option is incorrect.

Option 4)

\; \left ( \frac{1}{2},\frac{3}{2} \right )\;

This option is incorrect.

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