CAIE A-Level Mathematics 1.3.4 Lines and Circles

CAIE A-Level Mathematics 1.3.4 Lines and Circles
Cambridge International AS & A Level Mathematics 9709 syllabus for exams in 2028, 2029 and 20302028–2030

Practise solving line–circle intersections, constructing tangents from radius gradients and applying chord, centre and triangle geometry to coordinates, areas and distances.

How this is tested

  • substitute a line into a circle equation and solve the resulting quadratic for intersections
  • find a tangent gradient as the negative reciprocal of the radius gradient at contact
  • use centres, chords and radii to calculate triangle areas, tangent intersections or distances

Question 10

[Maximum number: 7]

A circle has equation x2+y2+4y−21=0x^{2}+y^{2}+4 y-21=0 and a straight line has equation 2 x+y-8=0. The line intersects the circle at two points.

Question 10(a)

(a)

Find the coordinates of these two points of intersection.

[ 4 ]

Question 10(b)

(b)

The circle has centre C and the two points of intersection are denoted by A and B.

Find the area of the triangle ABC.

[ 3 ]