if x=9 is the chord of contact of the hyperbola x^2-y^2=9 , then the equation of the corresponding pair of - Maths - Conic Sections

Question

if x=9 is the chord of contact of the hyperbola x^2-y^2=9 , then
the equation of the corresponding pair of tangents is

Manbar Singh · Accepted Answer

Dear Student,

The equation of chord of contact is,x = 9   
1The equation of the given hyperbola is,x2 - y2 = 9   
2POINTS OF INTERSECTION OF 1 AND 2 :Put x = 9 in 2, we get   92 - y2 = 9⇒y2 = 72⇒y = ±62So, points of intersection are 9, 62 and 9, -62Now, equation of tangent to the hyperbola x2 - y2 = 9  at  9, 62 isx×9 - y×62 = 9⇒3x - 22y - 3 = 0    
3Now, equation of tangent to the hyperbola x2 - y2 = 9  at  9, -62 isx×9 - y×-62 = 9⇒3x + 22y - 3 = 0    
4Now, joint equation of the pair of tangents is,   3x - 22y - 33x + 22y - 3 = 0⇒3x-32 - 22y2 = 0⇒9x2 + 9 - 18x - 8y2 = 0⇒9x2 - 8y2 - 18x + 9 = 0

Regards

if x=9 is the chord of contact of the hyperbola x^2-y^2=9 , then the equation of the corresponding pair of tangents is