2025 Presbyterian High School Prelims A Math Paper 2
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]
Solution:
Solution locked
Sign in to view the step-by-step solution
Similar questions are unavailable for this question.
Answer:a \((2,-3)\) b \((x-2)^2+(y+3)^2=25\) c(i) \((-6,-6)\) c(ii) The x-axis is tangent because its distance from \(C\) is \(6\), equal to the radius.