Explain why the graph of $y = -4x^2 + 4kx - (k^2 + 1)$ lies entirely below the $x$-axis.[3] Find

Question

Explain why the graph of $y = -4x^2 + 4kx - (k^2 + 1)$ lies entirely below the $x$-axis.[3] Find the range of values of $k$ for which the line $y = kx + 2$ meets the curve $x^2 + y^2 = 2$.[4]

Accepted Answer

(a) The graph lies entirely below the $x$-axis (b) $k\leq-1$ or $k\geq1$

2023 ACSBR AM S3 EOY Q7

2023 ACSBR AM S3 EOY Q7

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