Correct Answer - Option 1 :
\(\rm \sqrt{5}\)
Concept:
- Equation of Hyperbola , \(\rm \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\) , Eccentricity, e = \(\rm \sqrt{1+\frac{b^{2}}{a^{2}}}\)
- Equation of Hyperbola , \(\rm -\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\) , Eccentricity, e = \(\rm \sqrt{1+\frac{a^{2}}{b^{2}}}\)
Calculation:
Equation of give Hyperbola is \(\rm \frac{x^{2}}{4}-\frac{y^{2}}{16}=1\),
On comparing with standard equation , a = 2 and b = 4
We know that Eccentricity, e = \(\rm \sqrt{1+\frac{b^{2}}{a^{2}}}\)
⇒ e = \(\rm \sqrt{1+\frac{4^{2}}{2^{2}}}\)
⇒ e = \(\rm \sqrt{5}\) .
The correct option is 1.
