<p>A curve \(C\) has equation \(y = \sqrt{k^2 + k - x^2}\) and a line \(L\) has equation \(y = x + k\), where&nbsp;\(k\) is a constant. Given that&nbsp;\(C\) and \(L\) intersect at two distinct points, find the range of possible values of \(k\).<span class="inline-marks">[4]</span></p>

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 \(k\).

2024 TJC H1 Q2

2024 TJC H1 Q2