2023 MI PU1 P1 Q3

2023 MI PU1 P1 Q3

3 marks
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  1. The curve \({C:x^2-(y+1)^2=1}\) undergoes a sequence of three transformations as follows:
    I: \( \qquad\,\,\,\, \) A scaling parallel to \(x\)-axis with a scale factor of \(4\),
    II: \( \qquad\,\, \) A scaling parallel to \(y\)-axis with a scale factor of \(\frac{1}{2}\),
    III: \( \qquad \) A translation of \(2\) units in the positive \(y\)-direction.
    Find the equation of the resulting curve.[3]

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Answer:(ii) \({{\left( \frac{x}{4} \right)}^{2}}-{{\left( 2y-3 \right)}^{2}}=1\)

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