$\text{ If }x=9\text{ is the chord of contact of the hyperbola }{x}^2-y^2=9,\text{ then the equation of the corresponding pair of }$$\text{ tangents is }$

detailed solution

Correct option is B

Let a pair of tangents be drawn from the point x1,y1 to the hyperbolax2−y2=9Then the chord of contact will be xx1−yy1=9-----iBut the given chord of contact is x=9-----iiAs (i) and (ii) represent the same line, these equations should be identical and, hencex11=−y10=99 or x1=1,y1=0Therefore, the equation of pair of tangents drawn from (1,0) to x2−y2=9 is x2−y2−912−02−9=(x⋅1−y⋅0−9)2 Using SS1=T2 or  x2−y2−9(−8)=(x−9)2 or  −8x2+8y2+72=x2−18x+81 or  9x2−8y2−18x+9=0