JEE PYQ: Hyperbola Question 21
Question 21 - 2019 (12 Jan Shift 2)
If the vertices of a hyperbola be at $(-2, 0)$ and $(2, 0)$ and one of its foci be at $(-3, 0)$, then which one of the following points does not lie on this hyperbola?
(1) $(-6, 2\sqrt{10})$
(2) $(2\sqrt{6}, 5)$
(3) $(4, \sqrt{15})$
(4) $(6, 5\sqrt{2})$
Show Answer
Answer: (4)
Solution
Centre $O(0,0)$, vertices $(\pm 2, 0)$, so $a = 2$. Focus at $(-3,0)$: $ae = 3$, $e = \frac{3}{2}$. $b^2 = a^2(e^2-1) = 4 \cdot \frac{5}{4} = 5$. Equation: $\frac{x^2}{4} - \frac{y^2}{5} = 1$. Check $(6, 5\sqrt{2})$: $\frac{36}{4} - \frac{50}{5} = 9 - 10 = -1 \neq 1$. So $(6, 5\sqrt{2})$ does not lie on it.
BETA
