jee-main 2021 Q66

jee-main · India · session3_22jul_shift1 Conic sections Tangent and Normal Line Problems
Let a line $L : 2 x + y = k , k > 0$ be a tangent to the hyperbola $x ^ { 2 } - y ^ { 2 } = 3$. If $L$ is also a tangent to the parabola $y ^ { 2 } = \alpha x$, then $\alpha$ is equal to:
(1) 12
(2) - 12
(3) 24
(4) - 24
Let a line $L : 2 x + y = k , k > 0$ be a tangent to the hyperbola $x ^ { 2 } - y ^ { 2 } = 3$. If $L$ is also a tangent to the parabola $y ^ { 2 } = \alpha x$, then $\alpha$ is equal to:\\
(1) 12\\
(2) - 12\\
(3) 24\\
(4) - 24