For the circle C with the equation x^2+y^2-16 x-12 y+64=0 match the List I with the List II given below. The correct match is array llll ( i ) & ( ii ) & ( iii ) & ( iv ) array

Step-by-step solution

Given equation of circle is C=x^2+y^2-16 x-12 y+64=0 (i) Equation of polar at (-5,1) w.r.t. to C is array cc x(-5)+y(1)-8(x-5)-6(y+1)+64=0 & -5 x+y-8 x+40-6 y-6+64=0 & -13 x-5 y+98=0 & 13 x+5 y=98 array (ii) On differentiating Eq. (i) w.r.t. to x , we get array rrrr & 2 x+2 y d y d x -16-12 d y d x +0=0 & (2 y-12) d y d x =(16-2 x) & d y d x = ( 8-x y-6 ) array At (8,0) ( d y d x )_ (8,0) = 8-8 0-6 =0 Equation of tangent at (8,0) is (y-0)=0(x-8) y=0 (iii) Slope of normal is aligned d y d x & = 6-y 8-x ( d y d x )_