Porisma

Worked solution

Undo a three-step transformation of an implicit curve

A reflects in the y-axis; B translates 4 units in the positive x-direction; C scales parallel to y by 2. A curve undergoes A,B,C in that order, giving y2=−4xy^2=-4x. Determine its equation before the transformations. marks

[2010/DHS/Promo/6(a)]

CJC · Review problems · Question 6

Answer

y2=x−4y^2=x-4.

Undo C first

Replace y in the final equation by 2y: (2y)2=−4x (2y)^2=-4x, so y2=−xy^2=-x.

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Undo B next

Replace x by x+4: y2=−(x+4)=−x−4y^2=-(x+4)=-x-4.

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Undo A last

Replace x by −x: y2=−(−x)−4=x−4y^2=-(-x)-4=x-4. This is the original implicit curve.

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Common mistakes

This is an implicit parabola; do not discard either sign of y by taking only a positive square root.

Solution notes

All printed substitutions and intermediate equations retained. No source figure.

Read the hint