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If the chord  y=mx+1 of the circle x^{2}+y^{2}=1   subtends an angle of measure 45° at the major segment of the circle then value of m is

  • Option 1)

    2\pm \sqrt{2}

  • Option 2)

    -2\pm \sqrt{2}

  • Option 3)

    -1\pm \sqrt{2}

  • Option 4)

    none of these


Answers (1)


As we learnt in 

Condition of tangency -

c^{2}=a^{2}\; (1+m^{2})


- wherein

If  y=mx+c  is a tangent to the circle x^{2}+y^{2}=a^{2}



Equation of circle x2+y2=1

Now, y=mx+1

\\ So, \: \: x^{2}+y^{2}=(y-mx)^{2} \\ \\ x^{2}\left ( 1-m^{2} \right )+2mxy=0

which represents pair of lines with angle=45^{\circ}

\tan 45^{\circ}=\pm \:\frac{2\sqrt{m^{2}-0}}{1-m^{2}} \: =\pm \frac{2m}{1-m^{2}}=1

On solving  m=\frac{-2\pm 2\sqrt{2}}{2} \: =-1\pm \sqrt{2}

Option 1)

2\pm \sqrt{2}

This option is incorrect

Option 2)

-2\pm \sqrt{2}

This option is incorrect

Option 3)

-1\pm \sqrt{2}

This option is correct

Option 4)

none of these

This option is incorrect

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