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Find horizontal and vertical tangents to a closed curve

The equation of a closed curve is (x+2y)2+3(x−y)2=27(x+2y)^2+3(x-y)^2=27.

(i) Show by differentiation that its gradient is dydx=y−4x7y−x\dfrac{dy}{dx}=\dfrac{y-4x}{7y-x}.

(ii) Find the equations of the tangents parallel to (a) the x-axis, (b) the y-axis.

CJC · Discussion · Question 7

Set the numerator to zero for a horizontal tangent and the denominator to zero for a vertical tangent; check the other is nonzero.

Read the worked solution