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

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False
Given circle is `x^(2)+y^(2)-14x-10y-151=0`
`therefore` Centre=(7,5)
and Radius=`sqrt(49+25+151)=sqrt(225)=15`
So, the distances between th point (2,-7) and centre of the circle is given by
`d_(1)=sqrt((2-7)^(2)+(-7-5)^(2))`
`=sqrt(25+144)=sqrt(169)=13`
`therefore` Shortest distance,d=`abs(13-15)=2`
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