Let x-2y= be a tangent to the hyperbola a^2x^2-y^2=b^2.

Question

Let $\lambda x-2y=\mu$ be a tangent to the hyperbola $a^2x^2-y^2=b^2$. Then $\dfrac{\lambda^2}{a^2}-\dfrac{\mu^2}{b^2}$ is equal to:

Accepted Answer

Substitute $y=\dfrac{\lambda x-\mu}2$ into $a^2x^2-y^2=b^2$ and set the resulting quadratic's discriminant to zero. This yields, after simplification,

$$\frac{\lambda^2}{a^2}-\frac{\mu^2}{b^2}=4.$$

Solutions · 1