Correct Answer - Option 2 : √2, 2
Concept:
The standard equation of a hyperbola:
\(\rm {x^2\over a^2}-{y^2\over b^2} = 1\)
Where 2a and 2b are the length of the transverse axis and conjugate axis respectively and center (0, 0)
The eccentricity = \(\rm \sqrt{a^2+b^2}\over a\)
Length of latus recta = \(\rm 2b^2 \over a\)
Distance from center to focus = \(\rm \sqrt{a^2+b^2}\)
Calculation:
Given hyperbola x2 - y2 = 1
Compare with standard equation of hyperbola,
So, a2 = 1, b2 = 1
The eccentricity e = \(\rm \sqrt{a^2+b^2}\over a\)
⇒ e = \(\rm \sqrt{1^2+1^2}\over 1\)
⇒ e = \( \boldsymbol {\rm\sqrt{2}}\)
Now length of latus recta (l)= \(\rm 2b^2 \over a\)
⇒ l = \(\rm 2\times{1^2 \over 1}\)
⇒ l = \( \boldsymbol {\rm2}\)