A curve $C$ has equation $y = \sqrt{k^2 + k - x^2}$ and a line $L$ has equation $y = x + k$,

Question

A curve $C$ has equation $y = \sqrt{k^2 + k - x^2}$ and a line $L$ has equation $y = x + k$, where $k$ is a constant. Given that $C$ and $L$ intersect at two distinct points, find the range of possible values of $k$.[4]

Accepted Answer

No real value of $k$; the stated two-point intersection is impossible.

2024 TJC H1 Q2

2024 TJC H1 Q2

Solution:

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