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If theta denotes the acute angle between...

If `theta` denotes the acute angle between the curves, `y-10-x^(2)` and `y=2+x^(2)` at a point of their intersection, then `|tan theta|` is equal to `8/(3k)`. The vlaue of k is _____________.

Text Solution

Verified by Experts

The correct Answer is:
5
Point of intersection of the curves is `(+-2,6)`
Slope of tangents is `(dy)/(dx)|_(x=2)` Therefore slopes are -4 and +4
So `|tan theta|=|(2xx4)/(1-4^(2))|=8/15`
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