Question

Find the shortest distance from the point $(2,-7)$ to the circle $x^2+y^2-14x-10y-151=0$

• A. $28$
• B. $15$
• C. $2$
• D. $7$

Answer 1

The correct option is C $2$

$P(2,-7)$ is the given point and circle is $x^2+y^2-14x-10y-151=0$
Centre of circle $C$ is $(7,5)$ and
radius $r=\sqrt{7^2+5^2+151}=\sqrt{225}=15$
Shortest distance from $P$ to the circle is $|CP-r|$
$CP=\sqrt{25+144}=13$
$\therefore$ Shortest distance of $P$ from circle is $2$
Hence, option C.