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Question

Two tangents are drawn from a point (2,1) to the curve, y2=4x. If α is the angle between them, then |tanα| is equal to :

A
13
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B
13
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C
3
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D
3
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Solution

The correct option is B 3
Given parabola y2=4x
Let the equation of tangent to the parabola be
y=mx+1m
Since, P(-2,-1) lies on this line
1=2m+1m
2m2m1=0
m=1,12
Let m1=1 ,m2=12
Now, |tanα|=|m1m21+m1m2|
|tanα|=3

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