Consider the following statements in respect of hyperbola \frac{x^2}{\cos ^2 \theta}-\frac{y^2}{ \sin ^2 \theta}=1 : 1. The two foci are independent of \theta. 2. The eccentricity is \sec \theta. 3. The distance between the two foci is 2 units. How many of the statements given above are correct? [NDA II 2023]

UPSC NDA II 2023 Mathematics Solved Paper

Question : 86 of 120

Marks: +1, -0

Consider the following statements in respect of hyperbola ‌

cos2θ

−‌

sin‌2θ

=1 :
1. The two foci are independent of θ.
2. The eccentricity is secθ.
3. The distance between the two foci is 2 units.
How many of the statements given above are correct?

[NDA II 2023]

Only one
Only two
All three
None

Validate

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