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Question

If m1 and m2 are the slopes of the tangents to the hyperbola x225y216=1 which passes through the point (6,2), then

A
m1m2=2011
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B
m1+m2=2411
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C
m1+m2=4811
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D
m1m2=1120
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Solution

The correct options are
A m1+m2=2411
B m1m2=2011
Suppose the tangent y=mx+25m216 passes through the point (6,2).

2=6m+25m216

26m=25m216

Squaring both sides, we get

(26m)2=25m216

4+36m224m=25m216

4+36m224m25m2+16=0

11m224m+20=0

Let m1 and m2 be the roots of the above quadratic equation,

Sum of the roots=m1+m2=2411=2411

And Product of the roots=m1m2=2011

Hence m1+m2=2411 and m1m2=2011


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