C4

I don't know what method i need to use to do these sort of question. They're normally related to the equation of a curve, but it's the first part that i can't do:

'a curve C is described by the equation:

3x^2 + 4y^2 - 2x + 6xy - 5 = 0

Find an equation of the tangent to C...'

Reply 1

mrsmann

Differentiate implicitly and plug in the values of x and y to find the gradient at that point. The gradient you find will be the same as the gradient of the tangent at that point, so just say y = mx + c and find the intercept with your values of m, x and y.

Reply 2

mensandan

3x^2 + 4y^2 - 2x + 6xy - 5 = 0

Use Implicit Differentiation:

6x + 8y dy/dx - 2 + 6y + 6x dy/dx = 0

Factorise and gather

(8y + 6x) dy/dx = 2 - 6x - 6y

Leaving dy/dx = (2 - 6x - 6y)/(8y + 6x)

dy/dx = (1 - 3x - 3y)/(4y + 3x)

I think this type of question always relies on this approach. From here it is straight forward I believe. Mensandan