JEE Main 2022 · 24 Jun · Shift 1, Mathematics question 15

Standard form. The hyperbola is $\dfrac{x^2}{b^2/a^2}-\dfrac{y^2}{b^2}=1$ and the line is $y=\dfrac\lambda2x-\dfrac\mu2$.

Tangency ($c^2=A^2m^2-B^2$): $\dfrac{\mu^2}4=\dfrac{b^2}{a^2}\cdot\dfrac{\lambda^2}4-b^2$.

Rearrange. Dividing by $b^2/4$: $\left(\dfrac\lambda a\right)^2-\left(\dfrac\mu b\right)^2=4$.

(D)