Question

If $x-y=1$ is a tangent to the hyperbola $\frac{x^2}{4}-\frac{y^2}{3}=1$, the point of contact is

• A. (4, 3)
• B. (3, 4)
• C. (2, 1)
• D. (5, 4)

Answer 1

The correct option is A (4, 3)

The tangent on a hyperbola $\frac{x^2}{4}-\frac{y^2}{3}=1$ at the point $(x_1,y_1)$ will be $\frac{x{x}_1}{4}-\frac{y{y}_1}{3}=1$

i.e. $3x{x}_1-4y{y}_1=12$

Comparing this to the given equation $x-y=1$, we get

$\frac{3x_1}{1}=\frac{4y_1}{1}=\frac{12}{1}$

$\Rightarrow x_1=4,y_1=3$

The point of contact is $(4,3)$