If the tangent at the point (4 2 , 16 11 2 ) on the ellipse 16 x^2+11 y^2=256 touches the circle x^2+y^2-2 x=15 , then =

Step-by-step solution

Equation of tangent at point (4 2 , 16 11 2 ) on the ellipse 16 x^2+11 y^2=256 is aligned & 16 x(4 2 )+11 y ( 16 11 2 )=256 & 4 x 2 + 11 y 2 =16 aligned Since, tangent (i) is tangent to the circle array ll & x^2+y^2-2 x-15=0 , so & |4 2 -16| 16 ^2 2 +11 ^2 2 =4 & ^2 2 -8 2 +16=11+5 ^2 2 & 4 ^2 2 +8 2 -5=0 . & 2 = 1 2 = 3 or (- 3 ) & = 6 array