CAIE IGCSE Additional Math 8.2 line-circle intersection problems

Use this line-circle page to substitute a line into a circle, solve for intersection coordinates and use repeated roots to show tangency.

Exam points

Substitute a line equation into a circle equation to find intersection points.
Use a repeated root or discriminant condition to show a line is tangent.
Find exact coordinates where a circle meets an axis or tangent line in context.

[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

All question bank results loaded

8.2. Solve line-circle intersection problems question 1