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The diagram shows a circle, centre the origin - OCR - GCSE Maths - Question 17 - 2017 - Paper 1
Question 17
The diagram shows a circle, centre the origin. (a) Write down the equation of the circle. (b) Point P has coordinates (8, –6). Show that point P lies on the circle... show full transcript
Worked Solution & Example Answer:The diagram shows a circle, centre the origin - OCR - GCSE Maths - Question 17 - 2017 - Paper 1
Step 1
Step 2
Step 3
Find the equation of the tangent to the circle at point P.
Answer
The gradient of the radius to point P can be calculated using the coordinates of the origin (0, 0) and point P (8, -6):
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Calculate the gradient of the radius: m_{radius} = rac{y_2 - y_1}{x_2 - x_1} = rac{-6 - 0}{8 - 0} = - rac{3}{4}
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The gradient of the tangent line is the negative reciprocal of the radius's gradient: m_{tangent} = rac{4}{3}
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Using the point-slope form of the equation of a line, the equation of the tangent line at point P (8, -6) is: y - (-6) = rac{4}{3}(x - 8)
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Rearranging the equation gives: y + 6 = rac{4}{3}x - rac{32}{3} y = rac{4}{3}x - rac{32}{3} - 6 y = rac{4}{3}x - rac{32}{3} - rac{18}{3} y = rac{4}{3}x - rac{50}{3}