If (2 x-k y+3=0,3 x-y+1=0 ) are conjugate lines with respect to (5 x^2-6 y^2=15 ), then (k= )

Step-by-step solution

We know that, If two lines (l₁ x+m₁ y+n₁=0 ) and (l₂ x+m₂ y+n₂=0 ) are conjugate lines with respect to the hyperbola ( x^2 a^2 - y^2 b^2 =1 , then a^2 l₁ l₂-b^2 m₁ m₂=n₁ n₂ ) For hyperbola, (5 x^2-6 y^2=15 x^2 3 - y^2 5 / 2 =1 ) Here, (a^2=3, b^2= 5 2 , l₁=2, l₂=3 ), and (m₁=-k, m₂=-1 ) ( array lc and & n₁=3, n₂=1 & 3 2 3- 5 2 (-k)(-1)=3 1 & 18- 5 2 k=3 15= 5 2 k k=6 array )