If the equation of the curve on reflection of the ellipse (x-4)^2 16 + (y-3)^2 9 =1 about the line x-y-2=0 is 16 x^2+9 y^2+k₁ x-36 y+k₂=0 , then (k₁+k₂ ) 66 is equal to

Step-by-step solution

(x-4)^2 16 + (y-3)^2 9 =1 any point P on the curve (4(1+ ), 3(1+ )) . The reflection of the point P about the line x-y-2=0 can be found using aligned & h -4(1+ ) 1 = k -3(1+ ) -1 = -2(4(1+ )-3(1+ )-2) 2 =-(4 -3 )+1 & ~h =4(1+ )-4 +3 +1=4+3 +1 & and k=3(1+ )+4 -3 =3+4 -1 & ( ~h -5 3 )^2+ ( k -2 4 )^2=1 aligned equation of image 16(x-5)^2+9(y-2)^2=144 aligned & 16 x^2+9 y^2-160 x-36 y+292=0 & k₁=-160 k₂=292 & k₁+k₂=132 aligned