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  • Help me please, If a point P has co-ordinates (0, -2) and Q is any point on the circle, x2 + y2 - 5x - y + 5 = 0,then the maximum value of (PQ)2 is :

 If a point P has co-ordinates (0, -2) and Q is any point on the circle, x2 + y2 - 5x - y + 5 = 0,

then the maximum value of (PQ)2 is :

  • Option 1)

    \frac{25 + \sqrt{6} }{2}

  • Option 2)

    14 + 5\sqrt{3}

  • Option 3)

    \frac{47 + 10\sqrt{6}}{2}

  • Option 4)

    8 + 5\sqrt{3}

 

Answers (2)

As we learnt in 

Greatest distance of a point A from a circle -

AC+r

- wherein

A is the point and circle has centre C and radius r.

 Q is point on the circle x^{2}+y^{2}-5x-y+5=0

r=\sqrt{\left ( \frac{5}{2} \right )^{2}+\left(\frac{1}{2} \right )^{2}-5}

=\frac{\sqrt{6}}{2}

PQ=Maximum distance =PC + r

=\frac{5}{2}\sqrt{2}+\frac{\sqrt{6}}{2}

PQ^{2}=\frac{(5\sqrt{2}+\sqrt{6})^{2}}{4}=\frac{50+6+20\sqrt{3}}{4}

PQ^{2}=14+5\sqrt{3}


Option 1)

\frac{25 + \sqrt{6} }{2}

This option is incorrect

Option 2)

14 + 5\sqrt{3}

This option is correct

Option 3)

\frac{47 + 10\sqrt{6}}{2}

This option is incorrect

Option 4)

8 + 5\sqrt{3}

This option is incorrect

Posted by

Vakul

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