A-level C4 Maths help please
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A-level C4 Maths help please

[From: ] [author: ] [Date: 12-04-19] [Hit: ]
......
A curve has equation:

x^3 - 2xy - 4x + y^3 - 51 = 0

find an equation of the normal to the curve at the point (4,3), giving your answer in the form: ax + by + c = 0, where a,b and c are integers.

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Differentiating implicitly:

3x^2 - 2xy' - 2y - 4 + 3y^2y' = 0

y' = (3x^2 - 2y - 4)/(2x - 3y^2)

Slope of tangent line at (4, 3) = (38)/(-19) = -2

Slope of normal line = 1/2

Eqn of normal line:

y - 3 = 1/2*(x - 4)

y = x/2 - 1

y - x/2 + 1 = 0

2y - x + 2 = 0
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