Equation of one of the tangents passing through (2,8) to the hyperbola 5 x^2-y^2=5 is

Step-by-step solution

Given hyperbola is 5 x^2-y^2=5 or It can be rewritten as x^2 1 - y^2 5 =1 Here, Equation of tangent is aligned & y=m x a^2 m^2-b^2 & y=m x 1 m^2-5 aligned But point (2,8) lies on it. aligned & 8=2 m m^2-5 & (8-2 m)= m^2-5 aligned On squaring both sides, we get array rlrl & 64+4 m^2-32 m & =m^2-5 3 m^2-32 m+69 & =0 & (3 m-23)(m-3) & =0 & m & =3, 23 3 array On putting m=3 in Eq. (i), we get aligned y & =3 x 3^2-5 =3 x 2 & y=3 x+2 and y=3 x-2 aligned