jee-main 2026 Q35

jee-main · India · session1_21jan_shift1 Conic sections Confocal or Related Conic Construction
Ellipse $E: \frac{x^{2}}{36} + \frac{y^{2}}{16} = 1$, A hyperbola confocal with ellipse and eccentricity of hyperbola is equal to 5. The length of latus rectum of hyperbola is, if principle axis of hyperbola is $x$-axis?
(A) $\frac{96}{\sqrt{5}}$ (B) $24\sqrt{5}$ (C) $18\sqrt{5}$ (D) $12\sqrt{5}$
Ellipse $E: \frac{x^{2}}{36} + \frac{y^{2}}{16} = 1$, A hyperbola confocal with ellipse and eccentricity of hyperbola is equal to 5. The length of latus rectum of hyperbola is, if principle axis of hyperbola is $x$-axis?

(A) $\frac{96}{\sqrt{5}}$
(B) $24\sqrt{5}$
(C) $18\sqrt{5}$
(D) $12\sqrt{5}$