A circle has the equation $x^2 + y^2 - 8x - 4y = 5$. Find the radius of the circle and the coordin

Question

A circle has the equation $x^2 + y^2 - 8x - 4y = 5$. Find the radius of the circle and the coordinates of its centre.[4] The line $y = x - 1$ intersects the circle at two points $M$ and $N$. Show that the coordinates of $M$ and $N$ are $(0, -1)$ and $(7, 6)$ respectively.[3] Determine if $MN$ is the diameter of the circle. Show your working clearly.[2] Find the equation of the tangent of the circle at point $N$.[3]

Accepted Answer

(a) centre $(4,2)$, radius $5$ (b) $M=(0,-1)$, $N=(7,6)$ (c) $MN$ is not a diameter (d) $y=-\dfrac34x+\dfrac{45}{4}$

2023 CSS AM S3 EOY Q11

2023 CSS AM S3 EOY Q11

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