OCR MEI C1 — Question 5

Exam BoardOCR MEI
ModuleC1 (Core Mathematics 1)
TopicCircles

5 A circle has equation \(( x - 2 ) ^ { 2 } + y ^ { 2 } = 20\).
  1. Write down the radius of the circle and the coordinates of its centre.
  2. Find the points of intersection of the circle with the \(y\)-axis and sketch the circle.
  3. Show that, where the line \(y = 2 x + k\) intersects the circle, $$5 x ^ { 2 } + ( 4 k - 4 ) x + k ^ { 2 } - 16 = 0$$
  4. Hence find the values of \(k\) for which the line \(y = 2 x + k\) is a tangent to the circle.