# 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) Option 2) Option 3) Option 4)

N neha
V Vakul

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)

This option is incorrect

Option 2)

This option is correct

Option 3)

This option is incorrect

Option 4)

This option is incorrect

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