The equation of a closed curve is (x+2y)² +3(x-y) = 27. (i) Show, by differentiation, that the gradient at the point (x, y) on the curve may be dy y-4x expressed in the form dx 7y-x (ii) Find the equations of the tangents to the curve that are parallel to (a) the x-axis, (b) the y-axis. [(ii)(a) y= +2 (b) x=±/7

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.