don steward
mathematics teaching 10 ~ 16

Saturday, 9 April 2016

generalising GCSE questions (12)

AQA asks students to find the point where the tangent to a given circle (at the point where x = 1) cuts the x-axis

the relationship between the equation of the circle and the x-coordinate of the intersection of the tangent and the x-axis prompts the question:
is this always true?

initially, at least, choose the tangent at the point where x = 1

so, the property is generally true
how can this relationship be extended to a more general case?

where the tangent is at the point where x = n?

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