JEE 2025 — Mathematics PYQ

Foci of hyperbola (1, 14) (1, −12)
 x = 1 be the transverse axis

$$SP-S^{\prime }P=2b$$
$$\Rightarrow 2b=|8-18|$$
$$\Rightarrow b=5$$
$$S{S}^{\prime }=2be$$
$$26=2be$$
$$be=13$$
$$e=\frac{13}{5}$$
$$\therefore LengthofLR$$
$$=\frac{2a^2}{b}$$
$$=\frac{2k^2({\lambda }^2-1)}{b}$$

$$=2(5)\frac{(144)}{25}=\frac{288}{25}$$