Question

The number of tangents to the hyperbola $\frac{x^2}{4}-\frac{y^2}{3}=1$ though $(4,1)$ is :

• A. $1$
• B. $2$
• C. $0$
• D. $3$

Answer 1

The correct option is C $0$

Since $\frac{x^2}{4}-\frac{y^2}{3}=1$ at $(4,1)$ is $=\frac{16}{4}-\frac{1}{3}-1>0$

$\therefore$ the point $(4,1)$ lies inside the hyperbola

Hence the number of tangents through $(4,1)$ is zero.