Find the equations of the tangents to the hyperbola x 2 − 9 y 2 = 9 that are drawn from (3, 2) . Find the area of the triangle that these tangents form with their chord of contact.
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
; x – 3 = 0 ; 8 sq. unit
Sol. Let tangent y = mx + 
It passes through (3, 2)
∴ (2 – 3m) 2 = (9m 2 – 1)
∴ m is not defined or m = 
∴ tangents are
x = 3 ........ (i)
5x – 12y + 9 = 0 ........ (ii)
Chord of contact is 3x – 18y = 9 ...... (iii)
by (i) & (iii) by (ii) & (iii)
x = 3, y = 0 x = – 5, y = – 
Area of triangle = 
= × 2 × (3 + 5) = 8 sq. unit.
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