Two tangents are drawn from the point (−2,−1) to the parabola y2=4x. If α is the angle between those tangents then tan α=
A
3
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B
13
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C
2
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D
12
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Solution
The correct option is A3 The equation to the pair of tangents is [−y−2(x−2)]2=(1+8)(y2−4x)⇒(−2x−y+4)2=−(y2−4x) ⇒4x2+y2+16−16x−8y+4xy=9y2−36x⇒4x2+4xy−8y2+20x−8y+16=0 ∴tanα=2√4+32|4−8|=2×64=3