CAIE IGCSE Additional Math 8.2 Solve Line Circle Intersection Problems Questions

Practise Cambridge IGCSE Additional Mathematics by finding circle-axis intersections and proving tangency with exact contact coordinates.

Exam points

Find exact intersections of a circle with a coordinate axis.
Verify tangency by showing the line meets the circle at one point or has the required radius relationship.
Determine the exact coordinates of the point of contact between a tangent and circle.

[Maximum number: 3]

Solutions to this question by accurate drawing will not be accepted.
A circle has centre (4,2) and meets the x-axis at (-2,0).

Find, in exact form, the coordinates of the points where the circle meets the y-axis.

$16+(y-2)^2=40$ oe
M1 FT their equation of the circle, providing it is the equation of a circle.
$(y-2)^2=24$ or $y^2-4y-20=0$
A1 for correct quadratic equation in any form.
$(0,2\pm\sqrt{24})$ isw or equivalent exact form
A1

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CAIE IGCSE Additional Math 8.2 Solve Line Circle Intersection Problems Questions question 1