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Question

Determine the position of the point (3, - 4) with respect to the hyperbola x29−y216=1

A
Inside
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B
Outside
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C
on the periphery
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D
None of these
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Solution

The correct option is B Outside
The given Hyperbola is x29y216=1 or x29y2161=0

Then any point P(x1,y1) will lie inside, on or the outside of the hyperbola x29y216=1 depending upon the value of (x219y21161)

If the value of x219y21161>0 then point P(x1,y1) lies inside of the hyperbola.

If the value of x219y21161=0 then point P(x1,y1) lies on the hyperbola.

If the value of x219y21161<0 then point P(x1,y1) lies outside of the hyperbola.

Now let the value of the term x219y21161 at given point (3,4) is (x219y21161)(3,4)

Then (x219y21161)(3,4)=329(4)2161

111=1 .....(<0)

As value of term x219y21161 at point P(3,4) is less than 0, Hence the point lies outside of the hyperbola.

So correct option is B

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