OCR C1 — Question 8

Exam BoardOCR
ModuleC1 (Core Mathematics 1)
TopicCircles

8. The circle \(C\) has the equation $$x ^ { 2 } + y ^ { 2 } + 10 x - 8 y + k = 0$$ where \(k\) is a constant. Given that the point with coordinates \(( - 6,5 )\) lies on \(C\),
  1. find the value of \(k\),
  2. find the coordinates of the centre and the radius of \(C\). A straight line which passes through the point \(A ( 2,3 )\) is a tangent to \(C\) at the point \(B\).
  3. Find the length \(A B\) in the form \(k \sqrt { 3 }\).