Let m 1 and m 2 be the slopes of the tangents drawn from the point P(4,1) to the hyperbola 
If Q is the point from which the tangents drawn to H have slopes |m 1 | and |m 2 | and they make positive intercepts 
and 
on the x-axis, then 
is equal to________.
Text Solution
Verified by Experts8
(8)
Given that 
Equation of tangent to the hyperbola is: 
Passes through (4,1)
4m 2 - m - 3
Equation of tangents with slopes 1 & 
y = x-3.......(i)
......(ii)
(i)&(ii) 
Q = (-4,-7)
(PQ) 2 = 8 2 + 8 2 = 128
On converting (i) and (m) in intercept form we get,
Hence this is the required option.
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