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Question

If θ is the acute angle between the tangents drawn from (1,4) to the parabola y2=12x, then the value of sinθ+2cosθ is equal to

A
5
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B
3
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C
2
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D
1
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Solution

The correct option is A 5
Equation of tangent is y=mx+3m
Tangent passes through (1,4).
4=m+3m
m24m+3=0
m=1,3
Slope of tangents are m1=3,m2=1
tanθ=m1m21+m1m2=12
sinθ=15 and cosθ=25
sinθ+2cosθ=15+45=5

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