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Question

If the points (3sinθ,4cosθ) where θR, lies outside the hyperbola x24y25=1, then the value of θ is:

A
θR
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B
θR{π4}
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C
θR{π2,0}
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D
θR{π4,0,π2}
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Solution

The correct option is A θR
S<0 is the condition for the point to lie outside the hyperbola.
3sin2θ44cos2θ51<0
15sin2θ16cos2θ20<0
15(1cos2θ)16cos2θ20<0
1515cos2θ16cos2θ20<0
531cos2θ<0
31cos2θ+5>0
θR(0cos2θ1)

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