The product of the lengths of perpendiculars drawn from any point on the hyperbola x^2-2 y^2-2=0 to its asymptotes is :

Step-by-step solution

Equation of hyperbola is x^2-2 y^2=2 x^2 2 - y^2 1 =1 Here, a^2=2, b^2=1 Equation of asymptotes to the hyperbola x^2 a^2 - y^2 b^2 =1 is x^2 a^2 - y^2 b^2 =0 x a - y b =0 and x a + y b =0 Let P(a , b ) be any point, then the product of length of perpendiculars = [ a a + b b ] 1 a^2 + 1 b^2 [ a a + b b ] 1 a^2 + 1 b^2 = ^2 - ^2 1 a^2 + 1 b^2 = 1 1 2 + 1 1 = 2 3