Question

The sum of the miinimum and maximum distances of the point $(4,-3)$ to 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=$\sqrt{4+25+7}=6$

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Therefore minimum distance of point P from the cirlce is =CP−r=10-6=4

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

Hence sum =20