Question

Assertion :STATEMENT-1 : $\frac{5}{3}$ and $\frac{5}{4}$ are the ecentriceties of two conjugate hyperbola. Reason: STATEMENT-2 : If $e$ and $e_1$ are the eccentricities of two conjugate hyperbolas then $e{e}_1>1.$

• A. Statement -1 is True, Statement -2 is True ; Statement -2 is a correct explanation for Statement -1
• B. Statement-1 is True, Statement-2 is True ; Statement-2 is NOT a correct explanation for Statement-1
• C. Statement -1 is True, Statement -2 is False
• D. Statement -1 is False, Statement -2 is True

Answer 1

The correct option is B Statement-1 is True, Statement-2 is True ; Statement-2 is NOT a correct explanation for Statement-1

Eccentricity of hyperbola (or conjugate hyperbola) is greater than $1$

$\therefore e{e}_1>1$ is true.
Now we have the relation on between $e$ and $e_1$ is

$\frac{1}{e^2}+\frac{1}{e_1^2}=1$

Clearly $\frac{9}{25}+\frac{16}{25}=1$

Therefore, both statement are correct but reason is not explanation of assertion.
Hence, option 'B' correct.