Question:
A hyperbola has its centre at the origin, passes through the point $(4,2)$ and has transverse axis of length 4 along the $x$-axis. Then the eccentricity of the hyperbola is:
Correct Option: 1
Solution:
$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$
$2 a=4 \quad a=2$
$\frac{x^{2}}{4}-\frac{y^{2}}{b^{2}}=1$
Passes through $(4,2)$
$4-\frac{4}{b^{2}}=1 \Rightarrow b^{2}=\frac{4}{3} \Rightarrow e=\frac{2}{\sqrt{3}}$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.