OCR H240/03 2023 June — Question 4

Exam BoardOCR
ModuleH240/03 (Pure Mathematics and Mechanics)
Year2023
SessionJune
TopicCircles

4 A circle \(C\) has equation \(x ^ { 2 } + y ^ { 2 } - 6 x + 10 y + k = 0\).
  1. Find the set of possible values of \(k\).
  2. It is given that \(k = - 46\). Determine the coordinates of the two points on \(C\) at which the gradient of the tangent is \(\frac { 1 } { 2 }\).