Question

The sum of the minimum and maximum distances of the point $(4,-3)$ from the circle $x^2+y^2+4x-10y-7=0$ is

• A. $10$
• B. $12$
• C. $16$
• D. $20$

Answer 1

The correct option is D $20$

Let the given point be $P(4,-3)$ and center of the given circle is $C(-2,5)$

Thus $CP=\sqrt{(4+2{)}^2+(-3-5{)}^2}=10$

And the radius of the circle is $r=\sqrt{4+25+7}=6$

Therefore minimum distance of point P from the cirlce is $=CP-r=4$

And maximum distance is $=CP+r=10+6=14$

Hence sum $=20$