jee-main 2022 Q74

jee-main · India · session1_26jun_shift1 Tangents, normals and gradients Prove a given line is tangent to a curve

Let $S$ be the set of all the natural numbers, for which the line $\frac { x } { a } + \frac { y } { b } = 2$ is a tangent to the curve $\left( \frac { x } { a } \right) ^ { n } + \left( \frac { y } { b } \right) ^ { n } = 2$ at the point $( a , b ) , ab \neq 0$. Then
(1) $S = \phi$
(2) $n ( S ) = 1$
(3) $S = \{ 2k : k \in N \}$
(4) $S = N$

Let $S$ be the set of all the natural numbers, for which the line $\frac { x } { a } + \frac { y } { b } = 2$ is a tangent to the curve $\left( \frac { x } { a } \right) ^ { n } + \left( \frac { y } { b } \right) ^ { n } = 2$ at the point $( a , b ) , ab \neq 0$. Then\\
(1) $S = \phi$\\
(2) $n ( S ) = 1$\\
(3) $S = \{ 2k : k \in N \}$\\
(4) $S = N$

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