4MA1/1HR Jan 2023, Question 23: Equation of the Tangent Line
Pearson Edexcel International GCSE Mathematics A 4MA1 · Paper 1HR (Higher) · Calculator · 5 marks
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The question, in short
Find the equation of line Q through point G on y = 8x² − 14x − 6 where the gradient is 10, with Q perpendicular to the tangent at G, in the form ax + by + c = 0.
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Solution · 5 marks
- 1dy/dx = 16x − 14 = 10, so x = 1.5
- 2y = 8 × 1.5² − 14 × 1.5 − 6 = −9, so G is (1.5, −9)
- 3Q is perpendicular to gradient 10, so its gradient is −1/10
- 4y + 9 = −1/10 (x − 1.5), so 10y + 90 = −x + 1.5
- 5Multiply by 2 and rearrange: 2x + 20y + 177 = 0
Answer2x + 20y + 177 = 0
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