Question

The greatest distance of the point $(10,7)$ from the circle $x^2+y^2-4x-2y-20=0$ is:

• A. $5$
• B. $15$
• C. $10$
• D. $20$

Answer 1

The correct option is B $15$

$P(10,7)$ is the given point and circle is $x^2+y^2-4x-2y-20=0$
Centre of circle $C$ is $(2,1)$ and
radius $r=\sqrt{4+1+20}=\sqrt{25}=5$
Greatest distance from $P$ to the circle is $|CP+r|$
$CP=\sqrt{64+36}=10$
$\therefore$ Greatest distance of $P$ from circle is $15$
Hence, option B.