A tangent to the curve 9 b^2 x^2-4 a^2 y^2=36 a^2 b^2 makes intercepts of unit length on each of the coordinate axes, then the point (a, b) lies on

Step-by-step solution

Equation of given curve is, x^2 4 a^2 - y^2 9 b^2 =1 Let at point (2 a , 3 b ) on the curve (i). So, equation of tangent at point is x 2 a + y - 3 b =1 According to the question, 2 a= and 3 b=- So, 4 a^2-9 b^2=1 On taking locus of point (a, b) , we are getting 4 x^2-9 y^2=1 .