If θ denotes the angle between the curves y=30−2x2 and y=3+x2 at a point of their intersection, then 71|tanθ| is equal to
A
15
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B
13
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C
20
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D
18
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Solution
The correct option is D18 y=30−2x2⇒m1=−4x y=3+x2⇒m2=2x tanθ=∣∣∣m1−m21+m1m2∣∣∣=∣∣∣−4x−2x1−8x2∣∣∣=∣∣∣−6x1−8x2∣∣∣
For point of intersection, 30−2x2=3+x2 ⇒3x2=27⇒x2=9⇒x=±3 ⇒|tanθ|=∣∣∣−181−8×9∣∣∣=∣∣∣−18−71∣∣∣=1871 ⇒71|tanθ|=18