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

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

Let the hyperbola is, $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
Given, $2a=7\Rightarrow a=\frac{7}{2}$
Also hyperbola passes through $(5,2)$
$\Rightarrow \frac{25\times 4}{49}-\frac{4}{b^2}=1$
$\Rightarrow b^2=\frac{196}{51}$
Thus required hyperbola is, $\frac{4x^2}{49}-\frac{51y^2}{196}=1$
Hence, option 'C' is correct.