A few days ago
Find an equation of the tangent line to the following curve (piriform) at the point:?
(1,1/2*2^(1/2))
4*y^2=x^3*(3-x)
Top 1 Answers
A few days ago
Favorite Answer
4*y^2=x^3*(3-x)
4y^2 = 3x^3 – x^4
8y dy/dx = 9x^2 – 4x^3
dy/dx = (9x^2 – 4x^3) / 8y
The gradient at the point
(1,1/2*2^(1/2))
is:
(9 – 4) / 4sqrt(2)
= 5sqrt(2) / 8
The tangent is therefore:
y – (1/2)sqrt(2) = 5sqrt(2)(x – 1) / 8
8y – 4sqrt(2) = 5sqrt(2)x – 5sqrt(2)
8y – 5sqrt(2)x + sqrt(2) = 0.
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