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

Options

A. 0
B. 1
C. 2
D. 4

Answer

C

Explanation

We have , an equation of circle `x^(2)+y^(2)-10x-14y-151=0` let us compare this equation with `x^(2)+y^(2)+2gx+2fy+c=0` cleary, g=-5,f=-a and c=-151
`:.` centre of circle `=(-g,-f) =(5,7) ` and radius `=sqrt (g^(2)+f^(2)-c=)`sqrt (25+49+151=)`sqrt225=15` now, the distance between centre and the given point (-7,2)
`=sqrt((5+7)^(2)+(5)^(2))=sqrt((12^(2))+25)=sqrt169=13` clearly, the point (-7,2) lies inside the cilcle.
:. shortest distance = radius -distance between point and centre =15-13=2