The implicit equation 
<br />
<table width="100%"><tr><td align="center">
    <math xmlns="http://www.w3.org/1998/Math/MathML">
    <mstyle displaystyle="true"><mrow><mo stretchy="false">(</mo>
<msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow>
</msup>
<mo>+</mo><mn>2</mn><mi>ay</mi><mo>-</mo>
<msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow>
</msup>
<mo stretchy="false">)</mo><msup><mi></mi><mrow><mn>2</mn></mrow></msup>
<mo>=</mo>
<msup><mrow><mi>y</mi></mrow><mrow><mn>2</mn></mrow>
</msup>
<mo stretchy="false">(</mo>
<msup><mrow><mi>a</mi></mrow><mrow><mn>2</mn></mrow>
</msup>
<mo>-</mo>
<msup><mrow><mi>x</mi></mrow><mrow><mn>2</mn></mrow>
</msup>
<mo stretchy="false">)</mo></mrow>
    </mstyle></math>
</td></tr></table>
<br />

represents a family of functions the members of
the family corresponding to different values of

<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>a</mi></mrow></math>.
<br />
<br />
Re-arrange the equation into the form 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>y</mi><mo>=</mo><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></math>
and draw some graphs belonging to the family for
different values of 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>a</mi></mrow></math>. What is the domain of
the function 
<math xmlns="http://www.w3.org/1998/Math/MathML">
<mrow><mi>f</mi><mo stretchy="false">(</mo><mi>x</mi><mo stretchy="false">)</mo></mrow></math>?

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