Q:- The point on the circle 16(x2+y2)+48x-8y-43=0 nearest to the line 8x-4y+73=0 is _______________

Dear tapasranjan

16(x²+y²)+48x-8y-43=0

 x²+y²+3x-1/2 y- 43/16=0

 (x+3/2)² + (y-1/4)² =5

now find the equation of line perpendicular to the given line and passes through center of the circle.

 it will come  x+2y+1 =0

now find the point of intersection of this line to the given circle.

points will come (-7/2 ,5/4)  and (1/2,-3/4)

now find the length of perpendicual from these point to the given line . point which correspond to small length of pendicular is the desired point

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