Question

Area of the triangle formed by the lines x – y = 0, x + y = 0 and any tangent to the hyperbola x² – y² = a² is-

• A. |a|
• B. $\frac{1}{2}$|a|
• C. a²
• D. $\frac{1}{2}$a²

Answer 1

Answer: (C)

a²

Answer 2

x² – y² = a² … (1)

x – y = 0 …. (2)

x + y = 0 … (3)

Area of DCPQ = ?

D_CPQ = $\frac{1}{2}$ (PQ) (CA)

Q P (a, a) ; Q (a, –a)

CA = a ; PQ = 2a

\ D_CPQ = $\frac{1}{2}$ (2a) (1) = a²