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Difference between revisions of "2021 April MIMC Problems/Problem 18"

(Created page with "What can be a description of the set of solutions for this: <math>x^{2}+y^{2}=|2x+|2y||</math>? <math>\textbf{(A)}</math> Two overlapping circles with each area <math>2\pi</m...")
 
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What can be a description of the set of solutions for this: <math>x^{2}+y^{2}=|2x+|2y||</math>?
 
What can be a description of the set of solutions for this: <math>x^{2}+y^{2}=|2x+|2y||</math>?
  
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<math>\textbf{(A)}</math> Two overlapping circles with each area <math>2\pi</math>
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<math>\textbf{(A)}</math> Two overlapping circles with each area <math>2\pi</math>.
  
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<math>\textbf{(B)}</math> Four not overlapping circles with each area <math>4\pi</math>
+
<math>\textbf{(B)}</math> Four not overlapping circles with each area <math>4\pi</math>.
  
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<math>\textbf{(C)}</math> There are two overlapping circles on the right of the <math>y</math>-axis with each area <math>2\pi</math> and the intersection area of two overlapping circles on the left of the <math>y</math>-axis with each area <math>2\pi</math>
+
<math>\textbf{(C)}</math> There are two overlapping circles on the right of the <math>y</math>-axis with each area <math>2\pi</math> and the intersection area of two overlapping circles on the left of the <math>y</math>-axis with each area <math>2\pi</math>.
  
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<math>\textbf{(D)}</math> Four overlapping circles with each area <math>4\pi</math>
+
<math>\textbf{(D)}</math> Four overlapping circles with each area <math>4\pi</math>.
  
 
<math>\textbf{(E)}</math> There are two overlapping circles on the right of the <math>y</math>-axis with each area <math>4\pi</math> and the intersection area of two overlapping circles on the left of the <math>y</math>-axis with each area <math>4\pi</math>.
 
<math>\textbf{(E)}</math> There are two overlapping circles on the right of the <math>y</math>-axis with each area <math>4\pi</math> and the intersection area of two overlapping circles on the left of the <math>y</math>-axis with each area <math>4\pi</math>.

Revision as of 17:37, 22 April 2021

What can be a description of the set of solutions for this: $x^{2}+y^{2}=|2x+|2y||$?

$\textbf{(A)}$ Two overlapping circles with each area $2\pi$.

$\textbf{(B)}$ Four not overlapping circles with each area $4\pi$.

$\textbf{(C)}$ There are two overlapping circles on the right of the $y$-axis with each area $2\pi$ and the intersection area of two overlapping circles on the left of the $y$-axis with each area $2\pi$.

$\textbf{(D)}$ Four overlapping circles with each area $4\pi$.

$\textbf{(E)}$ There are two overlapping circles on the right of the $y$-axis with each area $4\pi$ and the intersection area of two overlapping circles on the left of the $y$-axis with each area $4\pi$.

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