JEE Main 2022 · 26 Jul · Shift 2 · Mathematics Q14

MathematicsSingle correct+4 / -1Question 14 of 90

If the line $x-1=0$ is a directrix of the hyperbola $kx^2-y^2=6$ , then the hyperbola passes through the point

\left(-2\sqrt5,6\right)

\left(-\sqrt5,3\right)

\left(\sqrt5,-2\right)

\left(2\sqrt5,3\sqrt6\right)

Answer and worked solution

Official answer: C

Directrix. $\frac{x^2}{6/k}-\frac{y^2}6=1$ has $e^2=1+k$ , and $\frac ae=1$ means $a^2=e^2$ : $\frac6k=1+k$ , so $k=2$ .

Check $2x^2-y^2=6$ : $(\sqrt5,-2)$ gives $10-4=6$ .

(C)

Topics:Hyperbola

JEE Main 2022 · 26 Jul · Shift 2, Mathematics question 14