Edexcel A-Level Maths 2020 Paper 2 (Pure) Q14 | Circles

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In this video, Lee Guffick works through Edexcel A-Level Maths 2020 Paper 2 (Pure) Question 14 (Circles), showing you how to form the circle equation, substitute the line 2x + y = 12, and prove the x-coordinates of the intersection points satisfy the required quadratic (3 marks).

Then, for Part (b), Lee uses the key tangent condition (discriminant = 0) to find the two possible values of the radius r, finishing neatly by completing the square.

If you’re revising circles + tangents + discriminant for Edexcel A-Level, this is exactly the sort of exam-style algebra that wins marks.

⏱️ TIMESTAMPS:
00:00 Introduction + what the question is asking
00:20 Sketching the circle in the first quadrant + the line 2x + y = 12
01:42 Finding the centre and equation of the circle: (x - r)^2 + (y - r)^2 = r^2
02:35 Substituting the line into the circle equation
03:01 Expanding and simplifying carefully
04:18 Arriving at the required quadratic in x (Part A complete)
05:46 Part B: Using the tangent condition (discriminant = 0)
06:12 Expanding b^2 - 4ac and simplifying
08:41 Dividing through by a common factor to clean it up
09:24 Completing the square to solve for r
10:20 Final answers + wrap-up

✏️ TOPICS COVERED:

Circle in the first quadrant touching both axes

Centre and radius reasoning from geometry

Forming the circle equation in coordinate geometry

Substitution of a line into a circle

Simplifying to a quadratic in x

Tangency condition using the discriminant (b^2 - 4ac = 0)

Solving a quadratic by completing the square

💯 EXAM TIPS:

Always sketch first (it clarifies the circle’s position and the centre immediately).

If a circle touches both axes in the first quadrant, the centre is (r, r).

For tangents, remember the golden rule: discriminant = 0.

Before solving, look for a common factor — it often turns a messy quadratic into something clean.

Completing the square is a quick, accurate method under exam pressure.

📚 ABOUT GUFFICK TUITION:
Lee Guffick is a former Head of Mathematics and A-Level Examiner, helping students achieve A/A grades* and secure places at top universities including Oxford, Cambridge, and the Ivy League.

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