Circle – Tangent Equation – Higher – GCSE Questions These questions are the same format as previous GCSE exams. COPY means they use the exact same numbers as the original GCSE question. Otherwise, they are clone questions using different numbers. The worksheets are provided in a variety of sizes.

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GCSE GCSE Edexcel Higher: June 2017 Paper 2, Q23 G is the circle with equation x2 + y2 = 4 1 G is the circle with equation x2 + y2 = 4 T 3 2 , 7 2 is a point on G. T 3 2 , 7 2 is a point on G. Find an equation of the tangent to G at point T. Find an equation of the tangent to G at point T. (Total for Question 1 is 3 marks) (Total for Question 1 is 3 marks)

GCSE GCSE Edexcel Higher: November 2017 Paper 3, Q19 Prove algebraically that the straight line with equation x – 2y = 10 is a tangent to the circle with equation x2 + y2 = 20 1 Prove algebraically that the straight line with equation x – 2y = 10 is a tangent to the circle with equation x2 + y2 = 20 (Total for Question 1 is 5 marks) (Total for Question 1 is 5 marks)

GCSE Edexcel Higher: June 2017 Paper 2, Q23 G is the circle with equation x2 + y2 = 4 T 3 2 , 7 2 is a point on G. Find an equation of the tangent to G at point T. (Total for Question 1 is 3 marks)

GCSE Edexcel Higher: November 2017 Paper 3, Q19 Prove algebraically that the straight line with equation x – 2y = 10 is a tangent to the circle with equation x2 + y2 = 20 (Total for Question 1 is 5 marks)

GCSE 𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑜𝑓 𝑅𝑎𝑑𝑢𝑠= 7 2 ÷ 3 2 = 7 2 × 2 3 = 7 3 Edexcel Higher: June 2017 Paper 2, Q23 1 G is the circle with equation x2 + y2 = 4 T 3 2 , 7 2 is a point on G. Find an equation of the tangent to G at point T. 𝐺𝑟𝑎𝑑𝑖𝑒𝑛𝑡𝑜𝑓 𝑅𝑎𝑑𝑢𝑠= 7 2 ÷ 3 2 Tangent 7 2 = 7 2 × 2 3 = 7 3 3 2 Gradient of tangent=negative reciprocal=− 3 7 Rationalise it = − 3 7 7 𝑥= 3 2 𝑦= 7 3 Tangent: y=− 3 7 7 𝑥+𝐶 7 2 =− 3 7 7 × 3 2 +𝐶 7 2 =− 9 7 14 +𝐶 7 2 + 9 7 14 =𝐶 7 7 14 + 9 7 14 = 𝐶= 16 7 14 = 8 7 7 y=− 3 7 7 𝑥+ 8 7 7 (Total for Question 1 is 3 marks)

GCSE Tangent = only one 1 solution x = 10 + 2y (10 + 2y)2 + y2 = 20 Edexcel Higher: November 2017 Paper 3, Q19 1 Prove algebraically that the straight line with equation x – 2y = 10 is a tangent to the circle with equation x2 + y2 = 20 Tangent = only one 1 solution x = 10 + 2y (10 + 2y)2 + y2 = 20 (10 + 2y) (10 + 2y) + y2 = 20 (100 + 20y + 20y + 4y2) + y2 = 20 5y2 + 40y + 100 = 20 5y2 + 40y + 80 = 0 y2 + 8y + 16 = 0 (y + 4) (y + 4) = 0 y = -4 x – (2 x -4) = 10 x – (-8) = 10 x + 8 = 10 x = 2 1 solution means line is tangent to circle. (Total for Question 1 is 5 marks)

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