2019 TJC P1 Q1
2019 TJC P1 Q1
5 marks
Prelims
The diagram below shows a shape which is symmetrical about the \(x\)- and \(y\)-axes. The shape is made up of four curves, \(A,\,B,\,C\) and \(D.\)
The curve \(A\) has equation \(\sqrt{x}+\sqrt{y}=1\) for \(0\le x\le 1\) and \(0\le y\le 1.\)
- State the equations and the range of values of \(x\) and \(y\) curves \(B\) and \(C.\)[3]
- The curves \(A\) and \(B\) are scaled by a factor \(\frac{1}{2}\) parallel to the \(x\)-axis and the curves \(C\) and \(D\) are scaled by a factor \(2\) parallel to the \(y\)-axis. Sketch the resulting shape.[2]
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Answer:(i) \(B:\sqrt{-x}+\sqrt y=1\), \(-1\le x\le0\), \(0\le y\le1\); \(C:\sqrt{-x}+\sqrt{-y}=1\), \(-1\le x\le0\), \(-1\le y\le0\). (ii) Sketch shown, with upper endpoints \((\pm\frac12,0)\), \((0,1)\) and lower endpoints \((\pm1,0)\), \((0,-2)\).
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