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Find minimum distance of ( 6 , 8 ) from circle x^2 + y^2 = 4

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Find minimum distance of ( 6 , 8 ) from circle x^2 + y^2 = 4

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Posted (Answer #1)

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`x^2+y^2 = 4 = 2^2`

The sortest distance from the given point lies in the extended radius of the circle.

Therefore,

The shortest distance to the point + radius = The distance to the center of the circle

The center of the circle = (0,0)

The radius is 2.

The distance to the center of the circle from (6,8) = d

`d = sqrt(6^2+8^2) = sqrt(36+64) = sqrt(100) = 10`

Therefore,

The shortest distance to the point + 2 = 10

The shortest distance to the point = 10-2 = 8

 

Therefore the distance from the point (6,8) to the circle is 8.

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