Question

The length of the transverse axis along x-axis with centre at origin 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

The correct option is C $\frac{4}{49}{x}^2-\frac{51}{196}{y}^2=1$

Let $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ represent the hyperbola.

Length of transverse axis, $2a=7$

$a=\frac{7}{2}$

Also, the point (5,-2) lies on the hyperbola, so,

$\frac{4}{49}\left(25\right)-\frac{4}{b^2}=1$

$\Rightarrow b^2=\frac{196}{51}$

Hence, the equation of the hyperbola is

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