CAIE P1 2021 June — Question 7

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2021
SessionJune
TopicCircles

7 The point \(A\) has coordinates \(( 1,5 )\) and the line \(l\) has gradient \(- \frac { 2 } { 3 }\) and passes through \(A\). A circle has centre \(( 5,11 )\) and radius \(\sqrt { 52 }\).
  1. Show that \(l\) is the tangent to the circle at \(A\).
  2. Find the equation of the other circle of radius \(\sqrt { 52 }\) for which \(l\) is also the tangent at \(A\).