If a directrix of a hyperbola centered at the origin and passing through the point (4,-2sqrt3 ) is 5x=4sqrt5 and its eccentricity is e , then :

Hyperbola: If a directrix of a hyperbola centered at the origin and passing… | JEE Main 2019

JEE Main 2019 (Online) 10th April Morning ShiftQuestion 1

If a directrix of a hyperbola centered at the origin and passing through the point $\left(4,-2\sqrt3\right)$ is $5x=4\sqrt5$ and its eccentricity is $e$, then :

Hyperbola

$4e^{4}+8e^{2}-35=0$$4e^{4}-24e^{2}+35=0$✓ Correct answer$4e^{4}-24e^{2}+27=0$$4e^{4}-12e^{2}-27=0$

Solution

$\frac ae=\frac4{\sqrt5}\Rightarrow a^2=\frac{16e^2}5$, $b^2=a^2(e^2-1)$. Substituting $(4,-2\sqrt3)$: $\frac5{e^2}-\frac{15}{4e^2(e^2-1)}=1$, i.e. $4e^4-24e^2+35=0$.

Hyperbola - JEE Mathematics question (JEE Main 2019 (Online) 10th April Morning Shift)

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