Coordinate Geometry of the Circle Structured Questions | Cambridge IGCSE Additional Mathematics

Question 1 of 24 · 10 marks

Coordinate Geometry of the Circle · 2 - Line-Circle Intersections

3 parts

Additional Mathematics 0606 · Question 1Paper 2 · Calculator[10 marks]

The circle $C$ has equation $x^2 + y^2 - 4x + 2y - 20 = 0$ .

(a)

Determine the centre and radius of circle $C$ .

[3]

(b)

The line $L$ has equation $y = 2x + k$ , where $k$ is a constant. Find the exact values of $k$ for which line $L$ is tangent to circle $C$ .

[4]

(c)

For $k = 5$ , line $L$ intersects circle $C$ at points $P$ and $Q$ . Calculate the exact length of the chord $PQ$ .

[3]