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What is the minimum distance of the point (3,4) from the circle is x^{2}+y^{2}-4x-2y-4=0

Option: 1

3+2\sqrt2


Option: 2

2\sqrt2-3


Option: 3

1


Option: 4

2


Answers (1)

best_answer

First, check if the point (4,3) lies inside or outside of the circle

\left(4\right)^2+\left(3\right)^2-4\left(4\right)-2\left(3\right)-4=-1<0

P(4,3) lies inside the circle

center of the circle is C(-g,-f) = (2,1)

CP = \sqrt{(2-4)^2+(1-3)^2}=\sqrt{(-2)^2+(-2)^2}=2\sqrt2

the radius of the circle is \sqrt{g^2+f^2-c}=\sqrt{2^2+1^2-(-4)}=3

minimum diistance = CP-r = 2\sqrt2-3

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shivangi.shekhar

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