The equation of one of the tangents drawn from the poin (0,1) to the hyperbola 45 x^2-4 y^2=5 is

Step-by-step solution

Let equation of tangent passing (0,1) and slope m be y-1=m(x-0) y=m x+1 Intersection with hyperbola 45 x^2-4 y^2=5 aligned & 45 x^2-4(m x+1)^2=5 & (45-4 m^2 ) x^2-8 m x-9=0 aligned For y=m x+1 to be tangent, discriminant =0 aligned & 64 m^2+4 (45-4 m^2 ) 9=0 & 16 m^2=405 m= 9 2 aligned Equation tangents are 9 x-2 y+2=0 and 9 x+2 y-2=0