Question

20. Use Barrow's a, e method to determine the slope of the tangent line to the curve x^3 + y^3=C^3

Answer 1

Answer: Slope would be,

$-\frac{x^2}{y^2}$

Step-by-step explanation:

Here, the given curve,

$x^3 + y^3=C^3$

$\implies x^3 + y^3 - C^3=0$

In Barrow's method,

Steps are as follows,

Step 1 : put, x = x - e, y = y - a

$(x-e)^3 + (y-a)^3 - C^3=0$

$x^3-3x^2e+3xe^2-e^3+y^3-3y^2a+3ya^2-a^3+C^3=0$

Step 2 : Reject terms which do not contain a or e,

$-3x^2e+3xe^2-e^3-3y^2a+3ya^2-a^3=0$

Step 3 : Reject all terms in which a or e have exponent greater than 1,

$-3x^2e-3y^2a=0$

Step 4 : Find the ratio of a : e,

$-3y^2a=3x^2e$

$\implies \frac{a}{e}=-\frac{x^2}{y^2}$

Hence, the slope of the given curve is $-\frac{x^2}{y^2}$