Points $P(-2, 0)$, $Q(5, 1)$, $R(6, -6)$ and $S(-1, -7)$ lie on a circle. $PQ$ and $SR$

Question

Points $P(-2, 0)$, $Q(5, 1)$, $R(6, -6)$ and $S(-1, -7)$ lie on a circle. $PQ$ and $SR$ are parallel chords of the same length. Show that the centre of the circle is at $(2, -3)$. [2] Find the equation of the circle.[3] A second circle has centre $C$. It is given that the $y$-axis is the perpendicular bisector of $CR$ and is also a tangent to the second circle. State the coordinates of $C$.[1] Hence explain why the $x$-axis is a tangent to the second circle.[2]

Accepted Answer

(a) Centre $(2,-3)$ (shown). (b) $(x-2)^2+(y+3)^2=25$ (c)(i) $C=(-6,-6)$. (ii) Radius and distance to the $x$-axis both equal $6$; tangent at $(-6,0)$.

2025 PHS P2 Q10

2025 PHS P2 Q10

Solution:

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