The line $L$ has equation $y = x - 1$ and the curve $C$ has equation $y^2 + kx^2 + 3x = k$.

Question

The line $L$ has equation $y = x - 1$ and the curve $C$ has equation $y^2 + kx^2 + 3x = k$. Find the set of values of $k$ if $L$ and $C$ do not intersect.[5] Write down the possible value(s) of $k$ if $L$ is a tangent to $C$.[1]

Accepted Answer

(a) $-\dfrac{\sqrt3}{2}<k<\dfrac{\sqrt3}{2}$. (b) $k=\pm\dfrac{\sqrt3}{2}$.

2024 RI H1 Q2

2024 RI H1 Q2

Solution:

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