Simultaneous Equations Structured Questions | Cambridge IGCSE Additional Mathematics

Question 1 of 3 · 10 marks

Simultaneous Equations · 1 - Integrated Circle-Line Intersections & Geometry

3 parts

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

The line $L$ has equation $x - 2y + 5 = 0$ . The curve $C$ is a circle with equation $x^2 + y^2 - 2x - 6y + 5 = 0$ .

(a)

Show that the line $L$ intersects the circle $C$ at the points $A(-1, 2)$ and $B(3, 4)$ .

[4]

(b)

Calculate the exact length of the chord $AB$ , giving your answer as a simplified surd.

[2]

(c)

Find the equation of the perpendicular bisector of $AB$ , and verify that it passes through the centre of the circle $C$ .

[4]