Question

The length of the transverse axis of a hyperbola is 7 and it passes through the point (5, -2). The equation of the hyperbola is

• A. $\frac{4}{49}x^{2} - \frac{196}{51}y^{2}$ = 1
• B. $\frac{49}{4}x^{2} - \frac{51}{196}y^{2}$ = 1
• C. $\frac{4}{49}x^{2} - \frac{51}{196}y^{2}$ = 1
• D. None of these

Answer 1

Answer: (C)

$\frac{4}{49}x^{2} - \frac{51}{196}y^{2}$ = 1

Answer 2

Trick: 2a = 7 or a = $\frac{7}{2}$

Also (5, -2) satisfies it, so $\frac{4}{49}$ (25) - $\frac{51}{196}$ (4) = 1

And a² = $\frac{49}{4}$⇒ a = $\frac{7}{2}$.