Hyperbola PYQs Set 11 (PDF)

Set 11 of 11 · Questions 301-302 of 302

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Mere Teacher · Previous Year Questions JEE Main Mathematics · Hyperbola · Set 11 (Q301-302)
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301. $The equations of the two tangents from (- 5, - 4) to the circle x^{2} + y^{2} + 4 x + 6 y + 8 = 0 are$ (1) $x - 7 y = 23, 6 x + 13 y = 4$ (2) $x + 2 y + 13 = 0, 2 x - y + 6 = 0$ (3) $2 x + y + 13 = 0, x - 2 y = 6$ (4) $3 x + 2 y + 23 = 0, 2 x - 3 y + 4 = 0$ 302. $Let the foci of the ellipse \frac{x ^{2}}{16} + \frac{y ^{2}}{7} = 1 and the hyperbola \frac{x ^{2}}{144} - \frac{y ^{2}}{α} = \frac{1}{25} coincide. Then the length of the latus rectum of the hyperbola is:-$ (1) $\frac{32}{9}$ (2) $\frac{18}{5}$ (3) $\frac{27}{4}$ (4) $\frac{27}{10}$