Question

Let the eccentricity of the hyperbola
$H : \frac{x²}{a²} - \frac{y²}{b²} = 1$
be √(5/2) and length of its latus rectum be 6√2, If y = 2 x + c is a tangent to the hyperbola H. then the value of c 2 is equal to

• A. 18
• B. 20
• C. 24
• D. 32

Answer 1

Answer: (B)

20

Answer 2

The correct answer is (B) : 20
$1 + \frac{b²}{a²} = \frac{5}{2} ⇒ \frac{b²}{a²} = \frac{3}{2}$
$\frac{2b²}{a} = 6\sqrt2 = 2 . \frac{3}{2} . a = 6\sqrt2$
$⇒ a = 2\sqrt2 , b² = 12$
$c² = a²m² - b² = 8.4 - 12 = 20$