Question

If a point p has a coordinates $(0,-2)$ and 'Q' is any point on the circle $x^2+y^2-5x-y+5=0$ then the maximum value of ${\left(PQ\right)}^2$

• A. $\frac{25+\sqrt{6}}{2}$
• B. $14+5\sqrt{3}$
• C. $\frac{47+10\sqrt{6}}{2}$
• D. $8+5\sqrt{3}$

Answer 1

The correct option is B $14+5\sqrt{3}$

REF.Image.

$r=\sqrt{\frac{25}{4}}+\frac{1}{4}-5={\left(\frac{3}{2}\right)}^{1/2}$

PQ = dix = PC+r

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

$P{Q}^2=14+5\sqrt{3}$